Answers:
(a) $349,809.29
(b) $53,409.29
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Work Shown for Part (a)
A = P*( (1+i)^n - 1 )/i
A = 1900*( (1+0.025/12)^(12*13) - 1 )/(0.025/12)
A = 349809.2943701
A = 349809.29
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Work Shown for Part (b)
interest = A - Pn
interest = 349809.29 - 1900*12*13
interest = 53409.29
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Notes:
- A = final account balance after 13 years
- P = deposit amount per month = 1900
- i = interest rate per month in decimal form = 0.025/12 = 0.002083333333333 approximately.
- n = number of months = 12*13 = 156 months (equivalent to 13 years).
- For more information about the formula in part (a), search out "future value of annuity formula". I'm using an ordinary annuity and not annuity due. This means I'm assuming the deposits happen at the end of the month.
- The answer to part (a) can be verified with a future value of annuity calculator.
