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

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

`\begin{gathered} A=P(1+(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\% = }(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+(r)/(n))^(nt) \\ 800,000=P(1+(0.06)/(12))^(12*10) \\ 800,000=P(1.005)^(120) \\ 800,000=1.8193967P \\ P=(800,000)/(1.8193967) \\ P=439,706.194916 \end{gathered}`

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