You are saving for your retirement by investing $900 per month in an annuity with a guaranteed interest rate of 6% per year. With a continuous stream of investment and continuous compounding, how much will you have accumulated in the annuity by the time you retire in 50 years?
A)$540,000.00
B)$3,795,396.65
C)$3,435,396.65
D)$188,961.67
E)$17,176.98

Question

Quizplus · Accepted Answer

We can use the formula for continuous compounding:

A = Pe^(rt)

where A is the accumulated amount, P is the principal investment (which starts at 0 in the first month), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate (6% or 0.06), and t is the time in years (50).

We can plug in these values and simplify:

A = 0*e^(0.06*50) + 900*(e^(0.06*50) - e^(0.06*0))
A = 3,435,396.65

Therefore, the answer is C, which represents the accumulated amount of $3,435,396.65 in the annuity after 50 years.

You Are Saving for Your Retirement by Investing $900 Per