Question

Assume that your parents wanted to have $70,000 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 11.5% 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 $ $110,000 saved just in​ case, how much would they have to save each year to reach their new​ goal?

Answer 1

future value of annuity = periodic payment*[(1+i)^n-1]/(i)

where - i - interest rate

n - no. of compounding periods

Case 1

interest rate = 11.5%

future value of annuity = 70000

assume on 18th birthday they will make the last payment.so no. of years = 18

70000 = x*[(1+0.1150)^18-1]/(0.1150)

x = (70000*0.1150)/[(1.1150)^18-1]

= 8050/(7.094922-1)

= 8050/6.095

= 1320.77

Case 2

110000 = x*[(1+0.1150)^18-1](0.1150)

x = (110000*0.1150)/[(1.1150)^18-1]

= 12650/6.094922

= 2075.50

Please comment in case of further clarification.