As Jorge starts working now at the age of 25, he decides to make regular contributions to a savings account.He wants to accumulate enough by age 55 to fund an annuity of $6,400 per month until age 80.
What should his monthly contributions be? Assume that both accounts pay 7.75%, compounded
Monthly.Round to the nearest cent.
A)$568.12
B)$598.02
C)$589.02
D)$612.02
E)$594.02

Question

Quizplus · Accepted Answer

To find the monthly contributions necessary to accumulate enough money to fund the annuity, we can use the present value formula for an annuity:
PV = PMT[(1 - (1 + r)^-n) / r]
where PV is the present value of the annuity, PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.

We can rearrange this formula to solve for PMT:
PMT = PV[r / (1 - (1 + r)^-n)]

Plugging in the given values, we get:
PV = $6,400[(1 - (1 + 0.0775/12)^-((80-55)*12)) / (0.0775/12)] = $1,710,200.63
r = 0.0775/12 = 0.00645833333
n = (55-25)*12 = 360

Then, we can solve for PMT:
PMT = $1,710,200.63[0.00645833333 / (1 - (1 + 0.0775/12)^-360)] = $598.019923

Therefore, Jorge's monthly contributions should be $598.02. Answer: B.

As Jorge Starts Working Now at the Age of 25