Question

Question

Suppose you have a savings goal of $550, 000 at the end of 25 years. You invest in an annuity that pays 6% interest,
compounded monthly. How much do you have to invest every month to reach your goal?

Answer 1

$794

Explanation:

Use the savings annuity formula.

A(t)=d((1+r/n)n⋅t−1)r/n

Substitute A(25)=$550,000, r=0.06 and n=12 compounding periods per year, into the formula to solve for d. Simplify.

$550,000=d((1+0.06/12)25⋅12−1)0.06/12,

simplifies to

$550,000$550,000d=d (1.005300−1)/0.005=692.99400d=$793.66

Rounded, the answer is $794.

Answer 2

You need to invest $260,045 each month to reach a savings goal of $550,000 at the end of 25 years.