SOLUTION: Suppose you want to have $400,000 for retirement in 25 years. Your account earns 10% annual interest compounded monthly. a) How much would you need to deposit in the account at

Algebra ->  Finance -> SOLUTION: Suppose you want to have $400,000 for retirement in 25 years. Your account earns 10% annual interest compounded monthly. a) How much would you need to deposit in the account at       Log On


   

Question 1202516: Suppose you want to have $400,000 for retirement in 25 years. Your account earns 10% annual interest compounded monthly.
a) How much would you need to deposit in the account at the end of each month?
301.47
b) How much interest will you earn?
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Part (a)

FV = $400,000 = future value needed
r = annual interest rate in decimal form
r = 0.10
i = monthly interest rate in decimal form
i = r/12 = 0.10/12 = 0.008333333 approximately
n = number of months = 25*12 = 300
P = unknown monthly payment

Future value of annuity formula
FV+=+P%2A%28+%281%2Bi%29%5En+-+1+%29%2Fi

400000+=+P%2A%28+%281%2B0.008333333%29%5E300+-+1+%29%2F0.008333333

400000+=+P%2A1326.833312406

P+=+400000%2F1326.833312406

P+=+301.469669370

P+=+301.47

Answer: $301.47

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Part (b)

total deposits = (number of months)*(monthly deposit)
= 300*301.47
= $90,441.

interest = 400,000 - 90,441 = 309,559

The reason for this very large interest amount is because 10% is fairly high on the interest rate scale. Average rates are usually somewhere around 3% to 5%.

Answer: $309,559