Question

A young, investing-savvy artist plans to retire in 30 years and is planning to save $1,000 every month. They plan to deposit the money at the beginning of each month into an account paying 5% compounded monthly. How much will they have in 30 years?

Answer 1

Ans:- In this question, we need to find the Future Value. This is a case of an annuity due. we will solve it by the formula method.

Note:- FV of annuity due means when the payment is done at the beginning of every period.

Future Value of an annuity due is calculated by P*[(1+r)^n-1]/r*(1+r), where P is the periodic payment, r is the rate of return and n is the number of periods.

P=$1000, r = 5%/12, n =30*12=360,

FV = $1000*[(1+(5%/12))^360-1] / (5%/12)* (1+(5%/12)) = $835,726.38.

Therefore, the FV in 30 years will be $835,726.38.

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