Answer to Question #161165 in Algebra for Ndlp

Question #161165

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?


1
Expert's answer
2021-02-24T06:42:32-0500

Solution: Given that PMT=$250                                       n=4 for querterly payment                                        t=35 years                                        r=11.5%=0.115a)We have to use the formula ,A=PMT[(1+rn)nt1rn]Substitute the given dataA=250[(1+0.1155)4(35)10.1154]Simplify,A=250[(1+0.1155)10510.1154]A=250[(1+0.02875)10510.0287]A=250[(1.02875)10510.0287]A=250[19.6125499710.0287]A=250[18.612549970.0287]A=250(647.39304)A=161848.26061b)Yanmei has contributed $250 to an RRSP at the end of each 3month period for the past 35 years. 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=161848.2606135000=126848.26061Solution:~ 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


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