Jim will retire in 30 years.He will invest $200 each month for 15 years and then let the accumulated value continue to grow for the next 15 years.How much will be available at retirement? Assume 11%,
Compounded monthly.Round to the nearest dollar.
A) $\quad \$ 469,966$
B) $\$ 422,933$
C) $\quad \$ 446,482$
D) $\$ 451,127$
E) $\quad \$ 469,924$

Question

Jim will retire in 30 years.He will invest $200 each month for 15 years and then let the accumulated value continue to grow for the next 15 years.How much will be available at retirement? Assume 11%,
Compounded monthly.Round to the nearest dollar. 
A) $\quad \$ 469,966$
B) $\$ 422,933$
C) $\quad \$ 446,482$
D) $\$ 451,127$
E) $\quad \$ 469,924$

Quizplus · Accepted Answer

To solve the problem, we need to use the formula for future value of an annuity with continuous compounding, which is:

FV = PMT * (e^(r*t) - 1) / (e^(r*t) - e^(-r*n))

where PMT is the monthly payment, r is the annual interest rate divided by 12, t is the number of years of payments, and n is the total number of compounding periods.

Substituting the given values, we get:

PMT = $200
r = 0.11/12
t = 15
n = 15*12 = 180

FV = 200 * (e^(0.11/12*15) - 1) / (e^(0.11/12*15) - e^(-0.11/12*180))
   = $469,966

Therefore, the best choice is A) \$469,966.

Jim Will Retire in 30 Years $469,966\quad \$ 469,966$469,966 B) $422,933\$ 422,933$422,933

Jim Will Retire in 30 Years $\quad \$ 469,966$ B) $\$ 422,933$