Question

Assume that your parents wanted to have $ 70 comma 000$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 5.0 %5.0% 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$110,000 saved just in​ case, how much would they have to save each year to reach their new​ goal?

Answer 1

Goal = $ 70,000

Interest rate = 5%

Let deposit each year(PMT) = x

no. of years to growth (n) = 17 years [ first birthday to eighteenth birthday]

Total amount = [ PMT × (((1 + r/n)^(nt) - 1) / (r/n)) ]

70,000 = x * (((1 + 0.05)^(17) - 1) / (0.05))

x = $ 2580

b)

Goal = $ 110,000

Interest rate = 5%

Let deposit each year(PMT) = x

no. of years to growth (n) = 22 years [ first birthday to eighteenth birthday + five year of graduation]

Total amount = [ PMT × (((1 + r/n)^(nt) - 1) / (r/n)) ]

110,000 = x * (((1 + 0.05)^(22) - 1) / (0.05))

x = $ 2721

Case ii)

if he has 70,000 at end of eighteenth year and wants 110,000 after 5 years,

then

Total amount = [ PMT × (((1 + r/n)^(nt) - 1) / (r/n)) ]

110,000 = [ 70000*(1+0.05)^(5) ] + [ x * (((1 + 0.05)^(5) - 1) / (0.05))

110000 - 89340 = X * 5.5256

x = 3739