Question

(1 point) (Exercise 2.11) A deposits $350 today and another $300 in five years into a fund paying simple interest of 7.3% per year. B will make the same two deposits, but the $350 will be deposited n years from today and the $300 will be deposited 2n years from today. B's deposits earn an annual effective rate of 7%. At the end of 8 years, the accumulated value of B's deposits equals the accumulated value of A's deposits. Calculate n. n = years.

Answer 1

Here, A"s amount after 8 years = Principal amount + interest on $350 for 5 years + interest on $ 650 for 3 years

= 350 + 300 + ( 350 * 5 * 7.3% ) + ( 650 * 3 * 7.3% )

= 650 + 127.75 + 142.35

= 920.1

Thus, after 8 years, total amount of B"s deposits should be $920.1 or interest should be amounted to 270.1 $.  

Interest on B"s deposiits after 8 years = 270.1

= ( 350 * (8-n) * 7% ) + ( 300 * (8-2n) *7% )

270.1 = (24.5 * (8-n) ) + ( 21 * (8-2n) )

270.1 = 196 - 24.5n + 168 - 42n

270.1 = 364 - 66.5n

66.5n = 93.9 OR

n = 1.41

Thus, B will depoit $350 after 1.41 years from A and then $ 300 after 2.82 years.