Question

Question 2>You want to have $800,000 when you retire in 10 years. If you can earn 6% interest compounded monthly,how much would you need to deposit now into the account to reach your retirement goal?$

Answer 1

SOLUTION

To solve this, we will apply the compound interest formula below

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ where\text{ } \\ P=\text{ money to be invested = ?} \\ A=\text{ amount after retiring 10 years later = \ 800,000} \\ r=\text{ interest rate = 6\% = }\frac{6}{100}=0.06 \\ n\text{ = number of times compounded = 12} \\ t=\text{ time in years = 10 years} \end{gathered}$

Substituting these values into the formula, we have

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 800,000=P(1+\frac{0.06}{12})^{12\times10} \\ 800,000=P(1.005)^{120} \\ 800,000=1.8193967P \\ P=\frac{800,000}{1.8193967} \\ P=439,706.194916 \end{gathered}$

Hence the answer is $439,706.19 to the nearest hundredth