You are saving for your retirement by investing $500 per month in an annuity with a guaranteed interest rate of 6% per year. You increase the amount you invest at the rate of 3% per year. With continuous investment and compounding, how much will you have accumulated in the annuity by the time you retire in 35 years Round your answer to the nearest cent.
A)$1,061,703.76
B) $130,012.45
C) $95,283.13
D) $10,617.04
E) $12,160,006.57

Question

You are saving for your retirement by investing $500 per month in an annuity with a guaranteed interest rate of 6% per year. You increase the amount you invest at the rate of 3% per year. With continuous investment and compounding, how much will you have accumulated in the annuity by the time you retire in 35 years  Round your answer to the nearest cent.  
A)$1,061,703.76
B) $130,012.45
C) $95,283.13
D) $10,617.04
E) $12,160,006.57

Quizplus · Accepted Answer

We can use the formula for continuous compound interest:

A = P*e^(rt)

where:
A = final amount
P = initial investment
r = annual interest rate
t = time (in years)

For the first year:
P = 500*12 = 6,000
r = 0.06
t = 1

A = 6,000*e^(0.06*1) = 6,000*1.061836 = 6,374.02

For the second year:
P = 500*12*1.03 = 6,180
r = 0.06
t = 1

A = 6,180*e^(0.06*1) = 6,180*1.061836 = 6,563.72

And so on, for 35 years.

Using a calculator or spreadsheet, we get:

A = 500*12*(e^(0.06*35) - 1)/(0.06 - 0.03*e^(0.06*35)) = $1,061,703.76 (rounded to the nearest cent)

Therefore, the answer is A.

You Are Saving for Your Retirement by Investing $500 Per