1. When their child was born, Elaine and Mike Porter deposited $5,000 in a savings account. The money ears interest at 6 percent compounded quarterly. How much will the account be worth when their child celebrates her second birthday?
My answer= $5,632.46
2. Asia Desai deposited $6,000 in a savings account that pays 5.5% interest compounded daily. How much interest did she earn in 21 days?
My answer= $18.96
3. Lincoln Coo has a check for $667.50 and a check for $126.25. He also has $482.00 in cash. He would lie to receive $25.00 in cash and deposit the rest in his savings account. What is the total deposit?
My answer= $1250.75.
4. Tom Newman took out a simple interest loan of $1,500.00 at 10 percent interest for 12 months. After 4 payments the balance is $1,100.00. He pays off the loan when the next payment is due. What is the interest?
I am not sure of this one.
5. Katherine o donnell obtained a personal loan of $1,800.00 at 10 percent interest for 12 months. the monthly payment is $165.00. what is the new principal after the first payment?
My answer= $1650.00
6. Rishi ram obtained an installment loan for $3,000.00. He agreed to repay the loan in 6 monthly payments. His monthly payments is $516.50. What is the APR?
My answer=6.6%
Am I correct with my answers? Thank you!!
1. P = Po(1+r)^n
Po = $5,000
r = (6%/4)/100 = 0.015 = Quarterly % rate expressed as a decimal.
n = 4comp./yr. * 2yrs. = 8 Compounding
periods.
Solve for P.
1. When their child was born, Elaine and Mike Porter deposited $5,000 in a savings account. The money earns interest at 6 percent compounded quarterly. How much will the account be worth when their child celebrates her second birthday?
To calculate the future value with compound interest, we can use the formula:
FV = P(1 + r/n)^(nt)
Where:
FV = Future Value
P = Principal amount (initial deposit)
r = Annual interest rate (6% or 0.06)
n = Number of compounding periods per year (quarterly = 4 times/year)
t = Number of years
Plugging in the values, we have:
FV = $5,000 (1 + 0.06/4)^(4 * 2)
FV = $5,000 (1 + 0.015)^(8)
FV = $5,000 * (1.015)^(8)
FV = $5,000 * 1.12550215625
FV = $5,632.51
Therefore, the account will be worth approximately $5,632.51 when their child celebrates her second birthday, which is slightly different from your answer.
2. Asia Desai deposited $6,000 in a savings account that pays 5.5% interest compounded daily. How much interest did she earn in 21 days?
To calculate the interest earned in this case, we can use the formula:
Interest = P(r/n)^(nt) - P
Where:
Interest = Amount of interest earned
P = Principal amount (initial deposit)
r = Annual interest rate (5.5% or 0.055)
n = Number of compounding periods per year (daily = 365 times/year)
t = Number of years
Plugging in the values, we have:
Interest = $6,000 (0.055/365)^(365 * 21) - $6,000
Interest = $6,000 (0.00015068493)^(7,665) - $6,000
Interest ≈ $19.29 - $6,000
Interest ≈ -$5,980.71
It seems there has been an error in your calculation since it does not make sense to earn a negative amount of interest. Therefore, please double-check your calculations.
3. Lincoln Coo has a check for $667.50 and a check for $126.25. He also has $482.00 in cash. He would like to receive $25.00 in cash and deposit the rest in his savings account. What is the total deposit?
To find the total deposit, we need to add up the amounts of the checks and the remaining cash after taking out $25.00.
Total deposit = $667.50 + $126.25 + ($482.00 - $25.00)
Total deposit = $667.50 + $126.25 + $457.00
Total deposit = $1,250.75
Therefore, the total deposit will be $1,250.75, which matches your answer.
4. Tom Newman took out a simple interest loan of $1,500.00 at 10 percent interest for 12 months. After 4 payments, the balance is $1,100.00. He pays off the loan when the next payment is due. What is the interest?
To find the interest, we need to calculate the total amount paid and subtract the principal loan amount.
Total amount paid = Principal + Interest
Balance after 4 payments = $1,100.00
Total amount paid after 4 payments = $1,100.00
Principal loan amount = $1,500.00
Interest = Total amount paid - Principal
Interest = $1,100.00 - $1,500.00
Interest = -$400.00
It seems there has been an error in your calculation since it does not make sense to have negative interest. Therefore, please double-check your calculations.
5. Katherine O'Donnell obtained a personal loan of $1,800.00 at a 10 percent interest rate for 12 months. The monthly payment is $165.00. What is the new principal after the first payment?
To find the new principal after the first payment, we need to subtract the amount paid from the initial principal amount.
Amount paid = Monthly payment
Initial principal = $1,800.00
New principal = Initial principal - Amount paid
New principal = $1,800.00 - $165.00
New principal = $1,635.00
Therefore, the new principal after the first payment will be $1,635.00, which matches your answer.
6. Rishi Ram obtained an installment loan for $3,000.00. He agreed to repay the loan in 6 monthly payments. His monthly payment is $516.50. What is the APR?
To calculate the APR (Annual Percentage Rate), we need to use the formula for the monthly payment on an installment loan:
Payment = [Principal * (r(1 + r)^n)] / [(1 + r)^n - 1]
Where:
Payment = Monthly payment
Principal = Loan amount
r = Monthly interest rate (unknown)
n = Number of monthly payments (6)
Plugging in the values, we can rearrange the formula to solve for the APR:
$516.50 = [$3,000 * (r(1 + r)^6)] / [(1 + r)^6 - 1]
Solving this equation for r and converting it to a percentage gives us the APR:
r ≈ 0.01721
APR ≈ 0.01721 * 12 * 100
APR ≈ 20.65%
Therefore, the APR for Rishi Ram's loan is approximately 20.65%, which is different from your answer.
1. To solve this problem, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the initial deposit
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $5,000, r = 0.06 (6% as a decimal), n = 4 (compounded quarterly), and t = 2 years.
Plugging in the values into the formula:
A = 5000(1 + 0.06/4)^(4*2)
A = 5000(1.015)^8
A ≈ $5,632.46
So your answer for the account value when the child celebrates her second birthday is correct.
2. To calculate the interest earned, you can use the formula for compound interest again:
I = P(1 + r/n)^(nt) - P
Where:
I = the interest earned
P = the initial deposit
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $6,000, r = 0.055 (5.5% as a decimal), n = 365 (compounded daily), and t = 21/365 years (since it's only 21 days).
Plugging in the values:
I = 6000(1 + 0.055/365)^(365*21/365) - 6000
I ≈ $18.96
So your answer for the interest earned in 21 days is correct.
3. To find the total deposit, you need to add up the checks and cash that Lincoln Coo has. Since he wants to receive $25.00 in cash and deposit the rest, you subtract $25.00 from the total amount.
Total deposit = $667.50 + $126.25 + $482.00 - $25.00
Total deposit = $1250.75
So your answer for the total deposit is correct.
4. To find the interest, you need to find the amount paid off when the loan is fully paid.
Initial loan = $1,500.00
Balance after 4 payments = $1,100.00
Since the balance is $1,100.00 and he pays off the loan when the next payment is due, the interest is the difference between the initial loan and the balance:
Interest = $1,500.00 - $1,100.00
Interest = $400.00
So the interest is $400.00.
5. To find the new principal after the first payment, you need to subtract the payment amount from the initial loan.
Initial loan = $1,800.00
Monthly payment = $165.00
New principal = $1,800.00 - $165.00
New principal = $1,635.00
So your answer for the new principal after the first payment is incorrect. It should be $1,635.00.
6. To find the APR, you can rearrange the formula for an installment loan:
APR = (Monthly payment / Loan amount) * 12 / Number of months * 100
In this case, the monthly payment is $516.50 and the loan amount is $3,000.00. The number of months is 6.
APR = (516.50 / 3000) * 12 / 6 * 100
APR ≈ 10.88%
So your answer for the APR is incorrect. It should be approximately 10.88%.