Question

For the last 10 years, Megan has made regular semiannual payments of $1,624.13 into an account paying 1.5% interest, compounded semiannually. If, at the end of the 10 year period, Megan stops making deposits, transfers the balance to an account paying 2.3% interest compounded monthly, and withdraws a monthly salary for 5 years from the new account, determine the amount that she will receive per month. Round to the nearest cent.
a.
$616.39
b.
$615.21
c.
$39,079.25
d.
$39,154.16

Answer 1

Answer: (a) $616.39

Work (outline):
- Semiannual rate r = 0.015/2 = 0.0075, number of semiannual deposits n = 20.
Future value after 20 deposits:
FV = 1624.13 * ((1+r)^n − 1)/r ≈ 1624.13 * ((1.0075)^20 − 1)/0.0075 ≈ $34,904.65.

- Transfer this to the monthly account with i = 0.023/12 ≈ 0.0019166667, and withdraw monthly for N = 60 months.
Monthly payment X satisfies
FV = X * (1 − (1+i)^−N)/i,
so X = FV * i / (1 − (1+i)^−N) ≈ 34,904.65 * 0.0019166667 / (1 − (1.0019166667)^−60) ≈ $616.39.

Thus the monthly salary is about $616.39.