CFA Level IQuantitative MethodsMedium
An investor plans to save for a down payment on a house. They deposit $1,500 at the end of each month into an account earning an annual interest rate of 6%, compounded monthly. How much will the investor have accumulated after 5 years?
- A$106,303.35
- B$90,000.00
- C$104,785.64
- D$99,033.72
Show answer & explanationAnswer & explanation
Correct answer: C. $104,785.64
This is a future value of an ordinary annuity calculation. The monthly payment, monthly interest rate, and total number of periods are used to find the accumulated amount.
Why the other options are wrong
- A. This result likely arises from an incorrect interest rate or period calculation, or compounding frequency.
- B. This represents only the sum of deposits without any interest.
- D. This value would be obtained if the deposits were made at the beginning of each period (annuity due) with slightly different compounding.
Future Value of Ordinary Annuity
The future value of an ordinary annuity is the total accumulated amount of a series of equal payments made at the end of each period, earning compound interest.
- Payments occur at the end of each period.
- Used to calculate the future worth of a stream of regular savings or investments.
- Formula: FV = PMT * [((1 + r)^n - 1) / r].
Memory trick: End-of-period payments grow to Future Value, like a 'house' built with 'monthly' 'bricks'.