Question

In: Finance

Assume that your parents wanted to have $130,000 saved for college by your 18th birthday and...

Assume that your parents wanted to have

$130,000

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

6.0 %

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

$170,000

saved just in​ case, how much would they have to save each year to reach their new​ goal?

Round to the nearest cent

Solutions

Expert Solution

Solution a
FV of annuity
The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
P = PMT x ((((1 + r) ^ n) - 1) / r)
Where:
P = the future value of an annuity stream $     130,000
PMT = the dollar amount of each annuity payment P
r = the effective interest rate (also known as the discount rate) 6%
n = the number of periods in which payments will be made 18
FV of annuity= PMT x ((((1 + r) ^ n) - 1) / r)
130000= PMT * ((((1 + 6%) ^ 18) - 1) / 6%)
Annual payment= 130000/ ((((1 + 6%) ^ 18) - 1) / 6%)
Annual payment= $    4,206.35
Solution b
FV of annuity
The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
P = PMT x ((((1 + r) ^ n) - 1) / r)
Where:
P = the future value of an annuity stream $     170,000
PMT = the dollar amount of each annuity payment P
r = the effective interest rate (also known as the discount rate) 6%
n = the number of periods in which payments will be made 18
FV of annuity= PMT x ((((1 + r) ^ n) - 1) / r)
170000= PMT * ((((1 + 6%) ^ 18) - 1) / 6%)
Annual payment= 170000/ ((((1 + 6%) ^ 18) - 1) / 6%)
Annual payment= $    5,500.61

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