Question 4.P.9: How much money must be deposited in a savings account each m......
How much money must be deposited in a savings account each month to accumulate $10 000 at the end of 5 years, if the bank pays interest at the rate of 6% per year, compounded (a) monthly? (b) semiannually? (c) quarterly? (d) daily?
In each case use (2.4), with the appropriate substitutions.
A/F = (F/A)^{-1} = \frac{i}{(1 + i)^n – 1} (2.4)(a) A = \$10 000\frac{0.06112}{(1 + 0.06112)^{(12)(5)} – 1} = \$10 000\frac{0.005}{0.34885} = \$143.33 per month
(b) A = \$10 000\frac{0.0612}{(1 + 0.0612)^{(2)(5)} – 1} = \$10 000\frac{0.03}{0.34392} = \$872.30 every 6 months
or $872.3016 = $145.38 per month.
(c) A = \$10 000\frac{0.0614}{(1 + 0.0614)^{(4)(5)} – 1} = \$10 000\frac{0.015}{0.34686} = \$432.45 per quarter
or $432.4513 = $144.15 per month.
(d) r = \frac{6\%}{12} = 0.005 \alpha = 30 \\\\ i = \left(1 + \frac{0.005}{30}\right)^{30} – 1 = .0050121 \\\\ A = \$10 000\frac{0.0050121}{(1 + 0.0050121)^{(12)(5)} – 1} = \$10 000\frac{0.0050121}{0.34982} = \$143.28 per month