Question

Luis invested his savings into a Registered Retirement Savings Plan (RRSP) at an interest rate of 3.50% compounded semi-annually. After one year, his investment grew to $24,600; however, the interest rate on the RRSP changed to 3.75% compounded quarterly and remained constant for the next two years.a. Calculate the original amount he invested into the RRSP.$__________Round to the nearest centb. Calculate the accumulated value of the investment at the end of three years (two years after the rate change).$__________Round to the nearest cent

Answer 1

The formula for the amount (A) is given as

`A=P(1+(r)/(n))^(nt)`

Given that, his savings plan was compounded semi-annually

Therefore,

`\begin{gathered} n=2 \\ r=3.50\text{ \%=}\frac{\text{3.50}}{100}=0.035 \\ t=1 \\ A=\text{ \$24600} \end{gathered}`

a) Hence, the original amount he invested into the RRSP will be calculated below

`\begin{gathered} 24600=P(1+(0.035)/(2))^(2*1) \\ 24600=P(1+0.0175)^2 \\ 24600=P(1.0175)^2 \\ 24600=P(1.03530625) \end{gathered}`
`\begin{gathered} (24600)/(1.03530625)=(P(1.03530625))/(1.03530625) \\ 23761.08519=P \\ \therefore P=23761.08519\approx\text{ \$23761.09(nearest cent)} \\ \therefore P=\text{\$23761.0}9 \end{gathered}`

Therefore, the original amount he invested into the RRSP is

`P=\text{\$23761.0}9`

b) The accumulated value of the investment at the end of three years will be,

Given that

`\begin{gathered} P=\text{ \$24,600} \\ r=3.75\text{ \%=}\frac{\text{3.75}}{100}=0.0375 \\ t=4 \end{gathered}`

Hence, the accumulated value of the investment at the end of three years will be

`\begin{gathered} A=24600(1+(0.0375)/(4))^(4*2)=24600(1+0.009375)^8=24600(1.009375)^8 \\ A=24600(1.077507625)=\text{ \$}26,506.68757\approx\text{ \$26,506.69(nearest cent)} \\ A=\text{\$26,506.69} \end{gathered}`

Therefore, the accumulated value of the investment at the end of three years is

`A=\text{\$26,506.69}`