Question 5.P.8: Mrs. Carter deposits $100 in the bank at the end of each mon......
Mrs. Carter deposits $100 in the bank at the end of each month. If the bank pays (a) 6% per year, (b) 7% per year, compounded continuously, how much money will she have accumulated at the end of 5 years? (Compare Problem 4.11.)
(a) The nominal monthly interest rate is 6%/12 = 0.5%. There will be a total of 5 × 12 = 60 monthly payments. Hence,
F = $100[F/A, 0.5%, 60]
From Appendix C, [F/A, 0.5%, 60] = 69.7970; therefore,
F = $100(69.7970) = $6797.70
(b) The nominal monthly interest rate is 7%/12=0.583333%. As a tabulated value of [F/A, 0.583333%, 60] is not available, we interpolate linearly between [F/A, 0.5%, 60] and [F/A, 0.75%, 60]:
[F/A, 0.583333%, 60] ≈ 69.7970 + \frac{0.583333 – 0.5}{0.75 – 0.5}(75.4912 – 69.7970) = 71.6951
The desired solution is then F = $100(71.6951) = $7169.51.
A more accurate procedure would be to use (5.4), with r replaced by r/12:
F/A = \frac{e^m – 1}{e^r – 1} (5.4) \\\\ F = \$100\frac{e^{(0.07)(5)} – 1}{e^{0.07/12} – 1} = \$100\frac{1.419068 – 1}{1.005850 – 1} = \$7163.56