1. Angelo wants to renovate his house in 3 years. He estimates the cost 300,000. How much must Angelo invest now at 8% compounded quarterly in order to have 300,000 3 years from now.
2. Angelo Ancis want to save 500,000 in 5.5 years to renovate their rest house. If the bank is paying 8% interest, compounded quarterly. How much must they deposit now in order to have money for the project?
3. Brian bought second hand truck for 125,000. He made down payment of 5,000 and agree to pay the balance in 24 equal monthly payments. If interest charge was 8% compounded monthly. How much brian should pay each month.
4. A debt of 25,000 was repaid in 10 equal quarterly payments. If the rate of interest was 7% compounded quarterly. What was the size if each payment.
5. RCBC bank pays an interest rate 4% annually compounded quarterly. How much money will CJ have in the bank at the end of 5 years if he deposits 2,500 at the end of each quarter?
1. P = Po(1+r)^n
P = $300,000
Po = Initial investment.
r = (8%/4)/100% = 0.02 = Quarterly % rate expressed as a decimal.
n = 4Comp/yr. * 3yrs. = 12 Compounding
periods.
P = Po*(1.02)^12 = 300,000
Po = 300,000/1.02^12 = $236,547.95
2. Same procedure as #1.
3. Po = 125,000 - 5000 = $120,000 =
Initial balance.
P = (Po*r*t)/(1-(1+r)^-t)
r = (8%/12)/100% = 0.006667 = Monthly %
rate.
t = 2yrs. * 12mo/yr. = 24 mo.
Plug the above values into the given Eq
and get:
P = $130,254.60
Amount/mo. = P/t
1. Angelo must invest a clown-sized amount of money now at 8% compounded quarterly in order to have 300,000 in 3 years. Maybe he could try investing a truckload of rubber chickens, a barrel of laughter, and a big red nose. It might not be the traditional investment strategy, but it'll certainly make him the talk of the town!
2. To have 500,000 for their rest house renovation in 5.5 years, Angelo Ancis must deposit an amount that will make any juggler jealous. With an 8% interest rate compounded quarterly, they might want to consider depositing a truckload of balloons, a sack full of laughter, and a bunch of silly hats. It would definitely make banking a whole lot more entertaining!
3. Oh, Brian! To pay off the balance of your second-hand truck with an 8% interest charge compounded monthly, you'll need to face the music and make some monthly payments. How about trying to find a way to magically pull out a bottomless pocket of coins? Alternatively, you could try saving up some belly laughs and exchanging them for monthly payment installments. That might make the process more enjoyable!
4. To repay a debt of 25,000 in 10 equal quarterly payments, you'll need to bring out your juggling skills. With a 7% interest rate compounded quarterly, make sure to keep your clown nose on tight while you juggle payments. Maybe you could try finding a clown car filled with money and make 10 grand exits to repay the debt in style!
5. With an interest rate of 4% annually compounded quarterly, RCBC bank might just be the perfect place for CJ to deposit his hard-earned money. If he deposits 2,500 at the end of each quarter, he might end up with a boatload of laughter and a giant piggy bank filled with cash at the end of 5 years. Who knows, CJ might even have enough money to start his own circus, complete with a clown orchestra and trapeze artists!
1. To calculate the amount Angelo must invest now, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = Future Value (300,000)
P = Principal Amount (unknown)
r = Annual Interest Rate (8% or 0.08)
n = Number of compounding periods per year (4, since it's compounded quarterly)
t = Number of years (3)
Plugging in the given values:
300,000 = P(1 + 0.08/4)^(4*3)
Simplifying:
300,000 = P(1 + 0.02)^12
Raising both sides to the power of 1/12:
(300,000)^(1/12) = P(1 + 0.02)
Calculating the left side:
(300,000)^(1/12) ≈ 1.4117
Dividing both sides by (1 + 0.02):
1.4117 ÷ (1 + 0.02) ≈ 1.3826
Therefore, Angelo must invest approximately 1.3826 times the principal amount to have 300,000 3 years from now.
To find the principal amount, we can divide the future value by 1.3826:
Principal Amount = 300,000 ÷ 1.3826 ≈ 216,778.46
So, Angelo must invest approximately 216,778.46 now.
2. Similar to the previous question, the formula for compound interest can be used:
A = P(1 + r/n)^(n*t)
Where:
A = Future Value (500,000)
P = Principal Amount (unknown)
r = Annual Interest Rate (8% or 0.08)
n = Number of compounding periods per year (4, since it's compounded quarterly)
t = Number of years (5.5)
Plugging in the given values:
500,000 = P(1 + 0.08/4)^(4*5.5)
Simplifying:
500,000 = P(1 + 0.02)^(22)
Dividing both sides by (1 + 0.02)^(22):
500,000 ÷ (1 + 0.02)^(22) ≈ 0.3811
Therefore, Angelo Ancis must deposit approximately 0.3811 times the principal amount to have 500,000 in 5.5 years.
To find the principal amount, we can divide the future value by 0.3811:
Principal Amount = 500,000 ÷ 0.3811 ≈ 1,312,428.85
So, Angelo Ancis must deposit approximately 1,312,428.85 now.
3. To calculate the monthly payment amount, we can use the formula for the present value of an annuity:
PMT = PV * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
PMT = Monthly Payment (unknown)
PV = Present Value (125,000 - 5,000 = 120,000)
r = Monthly Interest Rate (8% or 0.08 / 12)
n = Number of payments (24)
Plugging in the given values:
PMT = 120,000 * (0.08/12 * (1 + 0.08/12)^24) / ((1 + 0.08/12)^24 - 1)
Simplifying:
PMT = 120,000 * (0.0066667 * 1.008^24) / (1.008^24 - 1)
Calculating the numerator:
0.0066667 * 1.008^24 ≈ 0.1787
Calculating the denominator:
1.008^24 - 1 ≈ 0.1959
Dividing the numerator by the denominator:
0.1787 / 0.1959 ≈ 0.9123
Therefore, Brian should pay approximately 0.9123 times the present value each month.
To find the monthly payment amount, we can multiply the present value by 0.9123:
Monthly Payment = 120,000 * 0.9123 ≈ 109,476.92
So, Brian should pay approximately 109,476.92 each month.
4. To calculate the size of each payment, we can use the formula for the present value of an annuity:
PMT = PV * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
PMT = Payment Amount (unknown)
PV = Present Value (25,000)
r = Quarterly Interest Rate (7% or 0.07 / 4)
n = Number of payments (10)
Plugging in the given values:
PMT = 25,000 * (0.07/4 * (1 + 0.07/4)^10) / ((1 + 0.07/4)^10 - 1)
Simplifying:
PMT = 25,000 * (0.0175 * 1.0175^10) / (1.0175^10 - 1)
Calculating the numerator:
0.0175 * 1.0175^10 ≈ 0.1915
Calculating the denominator:
1.0175^10 - 1 ≈ 0.1772
Dividing the numerator by the denominator:
0.1915 / 0.1772 ≈ 1.0813
Therefore, the size of each payment is approximately 1.0813 times the present value.
To find the payment amount, we can divide the present value by 1.0813:
Payment Amount = 25,000 ÷ 1.0813 ≈ 23,107.18
So, each payment should be approximately 23,107.18.
5. To calculate the amount CJ will have in the bank at the end of 5 years, we can use the formula for the future value of an annuity:
A = PMT * ((1 + r/n)^(n*t) - 1) / (r/n)
Where:
A = Future Value (unknown)
PMT = Deposit Amount per Quarter (2,500)
r = Annual Interest Rate (4% or 0.04)
n = Number of compounding periods per year (4, since it's compounded quarterly)
t = Number of years (5)
Plugging in the given values:
A = 2,500 * ((1 + 0.04/4)^(4*5) - 1) / (0.04/4)
Calculating the numerator:
(1 + 0.04/4)^(4*5) - 1 ≈ 1.2214
Calculating the denominator:
0.04/4 ≈ 0.01
Multiplying the numerator by the reciprocal of the denominator:
1.2214 * (1/0.01) ≈ 122.14
Therefore, CJ will have approximately 122.14 times the deposit amount in the bank at the end of 5 years.
To find the future value, we can multiply the deposit amount by 122.14:
Future Value = 2,500 * 122.14 ≈ 305,350
So, CJ will have approximately 305,350 in the bank at the end of 5 years.
1. To find out how much Angelo must invest now, we can use the formula for compound interest:
Future Value = Present Value * (1 + (Interest Rate / Number of Compounding Periods)) ^ (Number of Compounding Periods * Number of Years)
In this case, the future value is 300,000, the interest rate is 8% (or 0.08), and there are 3 years, with quarterly compounding (so 4 compounding periods per year). We need to solve for the present value.
Rearranging the formula, we get:
Present Value = Future Value / [(1 + (Interest Rate / Number of Compounding Periods)) ^ (Number of Compounding Periods * Number of Years)]
Substituting the values into the formula, we get:
Present Value = 300,000 / [(1 + (0.08 / 4)) ^ (4 * 3)]
Simplifying the equation, we find:
Present Value ≈ 232,718.68
Therefore, Angelo must invest approximately 232,718.68 pesos now at 8% compounded quarterly to have 300,000 pesos 3 years from now.
2. Similar to the previous question, we can use the same formula for compound interest:
Present Value = Future Value / [(1 + (Interest Rate / Number of Compounding Periods)) ^ (Number of Compounding Periods * Number of Years)]
In this case, the future value is 500,000, the interest rate is 8% (or 0.08), there are 5.5 years, and quarterly compounding (so 4 compounding periods per year). We need to solve for the present value.
Substituting the values into the formula, we get:
Present Value = 500,000 / [(1 + (0.08 / 4)) ^ (4 * 5.5)]
Simplifying the equation, we find:
Present Value ≈ 376,666.35
Therefore, Angelo Ancis must deposit approximately 376,666.35 pesos now at 8% compounded quarterly in order to have 500,000 pesos for the project in 5.5 years.
3. To find out how much Brian should pay each month, we can use the formula for monthly installment payments with compound interest:
Loan Amount = Monthly Payment * [(1 - (1 + (Interest Rate / Number of Compounding Periods)) ^ (-Number of Compounding Periods * Number of Years))] / (Interest Rate / Number of Compounding Periods)
In this case, the loan amount is 125,000, the down payment is 5,000, the interest rate is 8% (or 0.08), there are 24 monthly payments, and the interest is compounded monthly (so 12 compounding periods per year). We need to solve for the monthly payment.
Substituting the values into the formula, we get:
Monthly Payment = (125,000 - 5,000) * [(1 - (1 + (0.08 / 12)) ^ (-12 * 2))] / (0.08 / 12)
Simplifying the equation, we find:
Monthly Payment ≈ 6,725.59
Therefore, Brian should pay approximately 6,725.59 pesos each month to repay the balance of 125,000 pesos in 24 equal monthly payments at 8% compounded monthly.
4. To find out the size of each payment, we can use the formula for installment payments with compound interest:
Loan Amount = Installment Payment * [(1 - (1 + (Interest Rate / Number of Compounding Periods)) ^ (-Number of Compounding Periods * Number of Years))] / (Interest Rate / Number of Compounding Periods)
In this case, the loan amount is 25,000, the interest rate is 7% (or 0.07), there are 10 equal quarterly payments, and the interest is compounded quarterly (so 4 compounding periods per year). We need to solve for the installment payment.
Substituting the values into the formula, we get:
Installment Payment = 25,000 * [(1 - (1 + (0.07 / 4)) ^ (-4 * 10))] / (0.07 / 4)
Simplifying the equation, we find:
Installment Payment ≈ 2,980.36
Therefore, the size of each payment should be approximately 2,980.36 pesos for a debt of 25,000 pesos repaid in 10 equal quarterly payments at a rate of 7% compounded quarterly.
5. To find out how much money CJ will have in the bank at the end of 5 years, we can use the formula for compound interest:
Future Value = Deposit Amount * [(1 + (Interest Rate / Number of Compounding Periods)) ^ (Number of Compounding Periods * Number of Years)]
In this case, the deposit amount is 2,500, the interest rate is 4% (or 0.04), there are 5 years, and the interest is compounded quarterly (so 4 compounding periods per year).
Substituting the values into the formula, we get:
Future Value = 2,500 * [(1 + (0.04 / 4)) ^ (4 * 5)]
Simplifying the equation, we find:
Future Value ≈ 3,785.54
Therefore, CJ will have approximately 3,785.54 pesos in the bank at the end of 5 years if he deposits 2,500 pesos at the end of each quarter, with an annual interest rate of 4% compounded quarterly.