What monthly deposit will produce a balance of Br 150,000 after 10 years? Assume that the annual percentage rate is 6% compounded monthly. Required: What is the total amount deposited over the 10-year period?
To find the monthly deposit required to produce a balance of Br 150,000 after 10 years, we can use the formula for the future value of a series of deposits:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future value (Br 150,000)
P = Monthly deposit
r = Monthly interest rate (6% / 12 = 0.005)
n = Total number of months (10 years * 12 months/year = 120 months)
Plugging in the values, we have:
150,000 = P * ((1 + 0.005)^120 - 1) / 0.005
Simplifying the equation, we find:
150,000 = P * (1.005^120 - 1) / 0.005
150,000 * 0.005 = P * (1.005^120 - 1)
750 = P * (1 + 0.7938)
P = 750 / 1.7938
P ≈ 417.89
Therefore, a monthly deposit of approximately Br 417.89 will produce a balance of Br 150,000 after 10 years.
To find the total amount deposited over the 10-year period, we can multiply the monthly deposit by the total number of months:
Total amount deposited = Monthly deposit * Total number of months
Total amount deposited = Br 417.89 * 120
Total amount deposited = Br 50,146.80
Therefore, the total amount deposited over the 10-year period is approximately Br 50,146.80.
To determine the monthly deposit required to produce a balance of Br 150,000 after 10 years, we can use the formula for calculating the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value (desired balance)
P = Monthly deposit
r = Monthly interest rate
n = Number of periods
In this case, the desired balance (FV) is Br 150,000, the annual percentage rate is 6%, compounded monthly, and the time period (n) is 10 years.
First, we need to express the annual interest rate as a monthly interest rate:
r = (1 + 0.06)^(1/12) - 1 = 0.004866
Now, let's plug in the values into the formula:
Br 150,000 = P * ((1 + 0.004866)^(12 * 10) - 1) / 0.004866
To solve for P, we can rearrange the formula:
P = (Br 150,000 * 0.004866) / ((1 + 0.004866)^(12 * 10) - 1)
Calculating this expression will give us the monthly deposit required.
Total Amount Deposited = Monthly deposit * Number of months (10 years * 12 months/year)
Hope this helps you in calculating the monthly deposit required and the total amount deposited over the 10-year period.
To find the required monthly deposit, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value
P = Monthly Deposit
r = Monthly interest rate
n = Number of periods
In this case, FV is given as Br 150,000, the annual interest rate is 6%, compounded monthly, so the monthly interest rate is (6%/12) = 0.5%. The number of periods is 10 years * 12 months = 120 months.
Substituting these values into the formula:
150000 = P * [(1 + 0.005)^120 - 1] / 0.005
Simplifying the equation:
150000 = P * (1.005^120 - 1) / 0.005
150000 * 0.005 = P * (1.005^120 - 1)
750 = P * (1.005^120 - 1)
Divide both sides of the equation by (1.005^120 - 1):
P = 750 / (1.005^120 - 1)
Using a calculator, we find:
P ≈ Br 845.62 (rounded to the nearest penny)
Therefore, a monthly deposit of Br 845.62 will produce a balance of Br 150,000 after 10 years.
To find the total amount deposited over the 10-year period, we can multiply the monthly deposit by the number of months:
Total amount deposited = Monthly deposit * Number of months
Total amount deposited = Br 845.62 * 120
Using a calculator, we find:
Total amount deposited ≈ Br 101,473.97 (rounded to the nearest penny)
Therefore, the total amount deposited over the 10-year period is approximately Br 101,473.97.