maria’s portfolio\ndetermine the rate of return after 10 years\n- a tax free savings account (tfsa) that…

maria’s portfolio\ndetermine the rate of return after 10 years\n- a tax free savings account (tfsa) that earns 2.8%, compounded monthly, and has a current balance of $5600.\n- the purchase at the end of each year of a 10 - year $500 csb that earns 3.2% compounded annually.\n- a savings account that earns 1.25% compounded monthly, where she saves $200 every month.

maria’s portfolio\ndetermine the rate of return after 10 years\n- a tax free savings account (tfsa) that earns 2.8%, compounded monthly, and has a current balance of $5600.\n- the purchase at the end of each year of a 10 - year $500 csb that earns 3.2% compounded annually.\n- a savings account that earns 1.25% compounded monthly, where she saves $200 every month.

Answer

Explanation:

Step1: Calculate future - value of TFSA

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times compounded per year, and $t$ is the number of years. For the TFSA, $P = 5600$, $r=0.028$, $n = 12$, and $t = 10$. $A_{1}=5600(1 +\frac{0.028}{12})^{12\times10}$ $A_{1}=5600(1+\frac{0.028}{12})^{120}$ $A_{1}\approx5600\times1.323197\approx7409.90$

Step2: Calculate future - value of CSB

We use the future - value of an ordinary annuity formula $FVA = A\times\frac{(1 + r)^{n}-1}{r}$, where $A$ is the annual payment, $r$ is the annual interest rate, and $n$ is the number of years. Here, $A = 500$, $r=0.032$, and $n = 10$. $FVA_{2}=500\times\frac{(1 + 0.032)^{10}-1}{0.032}$ $(1 + 0.032)^{10}=1.032^{10}\approx1.372677$ $FVA_{2}=500\times\frac{1.372677 - 1}{0.032}=500\times\frac{0.372677}{0.032}\approx5823.08$

Step3: Calculate future - value of savings account

First, we use the future - value of an ordinary annuity formula for compound interest $FVA=A\times\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}}$, where $A = 200$, $r = 0.0125$, $n = 12$, and $t = 10$. $FVA_{3}=200\times\frac{(1+\frac{0.0125}{12})^{12\times10}-1}{\frac{0.0125}{12}}$ Let $x=\frac{0.0125}{12}\approx0.001042$ and $m = 12\times10 = 120$ $(1 + x)^{m}=(1+0.001042)^{120}\approx1.133079$ $FVA_{3}=200\times\frac{1.133079 - 1}{0.001042}=200\times\frac{0.133079}{0.001042}\approx25535.41$

Step4: Calculate total initial investment

The initial investment in TFSA is $P_{1}=5600$. The annual investment in CSB is $A_{2}=500$ for 10 years, so total investment in CSB is $500\times10 = 5000$. The monthly investment in savings account is $A_{3}=200$ for 10 years (120 months), so total investment in savings account is $200\times120=24000$. $P_{total}=5600 + 5000+24000=34600$

Step5: Calculate total future value

$A_{total}=A_{1}+FVA_{2}+FVA_{3}=7409.90+5823.08 + 25535.41=38768.39$

Step6: Calculate rate of return

The rate of return $R$ is given by $R=\frac{A_{total}-P_{total}}{P_{total}}\times100%$ $R=\frac{38768.39 - 34600}{34600}\times100%$ $R=\frac{4168.39}{34600}\times100%\approx12.05%$

Answer:

The rate of return after 10 years is approximately $12.05%$