A couple has determined that they need $400,000 to establish an annuity when they retire in 20 years. How much money should they deposit at the end of each month in an investment plan that pays an annual rate of 8%, compounded monthly, so they will have the $400,000 in 20 years? Round your answer to the nearest cent.
A) $2,186.44
B) $679.09
C) $960.30
D) $18,762.78
E) $8,758.96

Question

A couple has determined that they need $400,000 to establish an annuity when they retire in 20 years. How much money should they deposit at the end of each month in an investment plan that pays an annual rate of 8%, compounded monthly, so they will have the $400,000 in 20 years? Round your answer to the nearest cent. ​
A) $2,186.44
B) $679.09
C) $960.30
D) $18,762.78
E) $8,758.96

Quizplus · Accepted Answer

The present value of an annuity formula is:

PMT*((1-(1/(1+r)^n))/r)

where PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

Plugging in the given values, we have:

PMT*((1-(1/(1+0.08/12)^(20*12)))/(0.08/12)) = 400,000

Solving for PMT, we get:

PMT = 679.09

Therefore, the couple should deposit $679.09 at the end of each month in the investment plan. Option B is the best choice.

A Couple Has Determined That They Need $400,000 to Establish