In: Finance
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
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 |