Answer to Question #161165 in Algebra for Ndlp

Question

Yanmei has contributed $250 to an RRSP at the end of each 3-month period for the past 35 years. During this time, the RRSP has earned an average of 11.5%/a compounded quarterly.

a) How much will the RRSP be worth at maturity?

b) How much of the investment will be interest earned over the 35 years?

Answer 1

$Solution:~ Given ~ that ~ PMT=\$250 \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~n=4 ~ for ~ querterly ~ payment \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~t=35~ years \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r=11.5\% =0.115 \\a) We~have ~ to ~ use ~ the ~ formula~, \\ A=PMT[\frac{(1+ \frac{r}{n})^{nt}-1}{\frac{r}{n}}] \\ Substitute~ the ~given ~data \\A=250[\frac{(1+ \frac{0.115}{5})^{4(35)}-1}{\frac{0.115}{4}}] \\ Simplify, \\A=250[\frac{(1+ \frac{0.115}{5})^{105}-1}{\frac{0.115}{4}}] \\A=250[\frac{(1+ 0.02875)^{105}-1}{0.0287}] \\A=250[\frac{(1.02875)^{105}-1}{0.0287}] \\A=250[\frac{19.61254997-1}{0.0287}] \\A=250[\frac{18.61254997}{0.0287}] \\A=250(647.39304) \\A=161848.26061 \\ b) Yanmei ~has ~contributed ~\$250~ to ~an~ RRSP ~at ~the ~end ~of ~each ~3-month ~\\period ~for ~the~ past ~35 ~years. \\ \therefore ~principle ~amount ~invested~ over ~35 ~year =[(35)(4)(250)]=\$35000 \\ \$35000~ of ~the~ investment ~will ~be~ interest~ earned ~over ~the~ 35 ~years. \\~ and~ \\ Interest ~ earned=161848.26061-35000=126848.26061$