Question

Eric wants to save $75,000 for his child’s college education in 12 years. Find the periodic deposit (payment) of an annuity earning 8% interest, compounded annually, needed to achieve a future balance of $75,000.

Answer 1

We can use the formula for the present value of an annuity to find the periodic deposit needed to achieve a future balance of $75,000 in 12 years at an annual interest rate of 8%, compounded annually.

The formula for the present value of an annuity is:

P = (PMT x [1 - (1 + r)^-n]) / r

Where:

PMT = periodic payment

r = interest rate per period

n = number of periods

P = present value

In this case, we want to solve for PMT. We know that the future value (FV) is $75,000, the interest rate (r) is 8%, compounded annually, and the number of periods (n) is 12.

First, we need to find the present value (P) of the annuity using the formula for future value:

FV = P x (1 + r)^n

$75,000 = P x (1 + 0.08)^12

$75,000 = P x 2.51817

P = $75,000 / 2.51817

P = $29,753.08 (rounded to the nearest cent)

Now we can plug in the values we know into the formula for the present value of an annuity and solve for PMT:

$29,753.08 = (PMT x [1 - (1 + 0.08)^-12]) / 0.08

$29,753.08 = (PMT x 6.71008) / 0.08

PMT = ($29,753.08 x 0.08) / 6.71008

PMT = $354.55 (rounded to the nearest cent)

Therefore, Eric needs to make a periodic deposit (payment) of $354.55, invested at an annual interest rate of 8%, compounded annually, to achieve a future balance of $75,000 for his child's college education in 12 years.

Answer 2

Interest = $72,000

Explanation:

We know the interest formula is:

Interest = Principal x Rate x Time

First, put in the numbers:

Interest = $75,000 x 8% x 12 years

Then calculate:

Percent means over a hundred, so 8% is 8 over 100:

Interest = $75,000 x
`(8)/(100)` x 12 years

Put $75,000 over 1, so you can multiply it with 8%:

Interest = $6,000 x 12 years

Finally, multiply:

Interest = $72,000

Therefore, to achieve the future balance of $75,000, Eric needs an interest of $72,000.