Question

help??
Sarat invested an average of $375 per month since age 35 in various securities for his retirement savings. His investments averaged a 4.5% annual rate of return until he retired at age 65. Given the same monthly investment and rate of return, how much more would Sarat have in his retirement savings had he started investing at age 25? Assume monthly compounding.

$202,500.00

$218,161.70

$117,562.50

$174,278.98

Answer 1

@Mertsj

Answer 2

so confused

Answer 3

No need to be confused. You just need the correct formula.

\(FV = A \times \dfrac {(1 + i)^n - 1}{i}\)

FV = future value
n = number of periods
i = interest rate per period as a decimal
A = annualized (monthly) payment

Use the above formula for both 30 years (n = 360) and 40 years (n = 480). Then find the difference. \(i = \dfrac{4.5}{12 \times 100} \), \(A = 375\).

Answer 4

So now what?

Answer 5

@mathstudent55

Answer 6

\(i = \dfrac{4.5}{12 \times 100} = 0.00375\),

\(A = $375\)

\(n = 360\)

Plug in those values in the formula. What do you get? That is calculating how much money was saved by retiring at 65 and starting at 35.

Answer 7

it looks like you plugged them in already..

Answer 8

@mathstudent55

Answer 9

\(FV = A \times \dfrac {(1 + i)^n - 1}{i}\)

This is the formula. Use a calculator to calcuate its value with those numbers above plugged in.

Answer 10

I'm sorry I am new to these problems I don't understand

Answer 11

@mathstudent55

Answer 12

Fill in the variables with the values you have and evaluate. You'll need a scientific calculator for this.

\(FV = A \times \dfrac {(1 + i)^n - 1}{i}\)

\(FV = $375 \times \dfrac {(1 + 0.00375)^{360} - 1}{0.00375} \)

Answer 13

Then you need to use the formula again for saving from age 25, which is 40 years, n = 480, of saving money.

\(FV = $375 \times \dfrac {(1 + 0.00375)^{480} - 1}{0.00375}\)

Then subtract the smaller amount from the larger amount.