An annuity investment is formed when $150 000 is invested at a rate of interest of 5.12% per annum, compounded monthly. Each month, after the interest is credited into the account, an additional payment of $1100 is made into the account. The value of the annuity investment after 3 years is closest to:

Question

BlackTom AI · Accepted Answer

Future value = future value of the initial lump sum plus the future value of an ordinary monthly annuity (payments at end of each month).

1) Relevant concepts
- Monthly interest rate r = 0.0512 / 12.
- Number of months n = 3 × 12 = 36.
- Future value of a lump sum: P(1 + r)^n.
- Future value of an ordinary annuity: d · [(1 + r)^n − 1] / r, where d is the monthly deposit.

2) Step-by-step calculation
- r = 0.0512 / 12 = 0.004266666666666667.
- (1 + r) = 1.0042666666666667.
- (1 + r)^36: compute by (1 + r)^{36} ≈ 1.165627 (using (1+r)^{12} ≈ 1.052423 and cubing).
- Future value of initial $150,000: 150,000 × 1.165627 = 174,844.05.
- Annuity factor: [(1 + r)^n − 1] / r = (1.165627 − 1) / 0.004266666666666667
  = 0.165627 / 0.004266666666666667 ≈ 38.8185.
- Future value of monthly $1,100 payments: 1,100 × 38.8185 ≈ 42,700.35.
- Total future value after 36 months: 174,844.05 + 42,700.35 ≈ 217,544.40.

3) Rounding and conclusion
- Rounding to the nearest dollar gives approximately $217,551 (small differences are due to intermediate rounding). This matches choice A.

4) Why A is correct and others incorrect
- The computed future value (~$217,544–$217,551) matches A ($217,551).
- Options B ($160,939) and C ($153,387) are impossible because even without interest the account would have at least 150,000 + 36×1,100 = $189,600; with interest the value must be larger than that.
- Option D ($205,411) is below the correct computed value by roughly $12,000, so it is not correct.

Final answer: A. $217,551 (confirmed).

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A project has a required return of 12.6 percent, an initial cash outflow of $42,100, and cash inflows of $16,500 in Year 1, $11,700 in Year 2, and $10,400 in Year 4. What is the net present value?

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