Question

Assume that your parents wanted to have $ 70 comma 000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 6.5 % per year on their investments. a. How much would they have to save each year to reach their​ goal? b. If they think you will take five years instead of four to graduate and decide to have $ 110 comma 000 saved just in​ case, how much would they have to save each year to reach their new​ goal?

Answer 1

This problem needs to be solved in a financial calculator. You can download it.

A fixed amount needs to be paid each year which will earn an interest of 6.5% for 18 years to reach a total of $70,000.

In financial calculator you need to input the below data.

N = 18 (No of years you are investing the amount)

I/Y = 6.5% (Your investment will earn a return of 6.5%)

PV = 0 (There is no initial lump sum amount that you have invested)

FV = 70,000 (You need your corpus to grow to 70,000)

CPT + PMT = This is what you are trying to calculate. This will throw you the payment that you need to do each year, which will fetch you the desired Future Value.

= 2159

So if they save 2159 each year for 18 years, then they will be able to save 70,000 by the end of 18 years.

Now if the Future value requirement changes from 70,000 to 110,000. Then obviously the investment made each year needs to change. So in that case, you just need to change the FV in calculator.

FV = 110,000 (Earlier FV was 70,000 now it is 110,000, rest I/Y, N remains same)

CPT + PMT = 3,394

So you see that the payment that you need to make each year increased from $2,159 to $3,394