Find the amount accumulated in an increasing annuity in which $100 is deposited monthly for 20 years at 5% per year in an account containing $10,000 at the start. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
A)$68,229.77
B) $41,103.37
C) $51,172.33
D) $40,937.86
E) $27,537.44

Question

Find the amount accumulated in an increasing annuity in which $100 is deposited monthly for 20 years at 5% per year in an account containing $10,000 at the start. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​
A)$68,229.77
B) $41,103.37
C) $51,172.33
D) $40,937.86
E) $27,537.44

Quizplus · Accepted Answer

We can solve this problem using the formula for the future value of an increasing annuity:

FV = Pmt x [(1 + r)^n - 1]/r + PV x (1 + r)^n

where:
- Pmt = the monthly deposit amount = $100
- r = the monthly interest rate = 5% / 12 = 0.00417
- n = the number of months = 20 years x 12 = 240
- PV = the present value = $10,000

Plugging in these values, we get:

FV = $100 x [(1 + 0.00417)^240 - 1]/0.00417 + $10,000 x (1 + 0.00417)^240
   = $100 x 319.872 + $10,000 x 2.653297
   = $68,229.77

So the answer is A.

Find the Amount Accumulated in an Increasing Annuity in Which