Question

Suppose someone wants to accumulate $130,000 for retirement in 30 years. The person has two choices. Plan A is a single deposit into an account with annual compounding and an APR of 5%. Plan B is a single deposit into an account with continuous compounding and an APR of 4.9%. How much does the person need to deposit in each account in order to reach the goal?The person must deposit $______ into the account for Plan A to reach the goal of 130,000  (Round to the nearest cent as needed

Answer 1

The plan A is a compounding, the formula for anual compunding is given by:

`f=P*(1+r^)^t`

P= INITIAL VALUE =?

r= Interest rate= 5%

t= time in years= 30 years

f= final amount=$130000

Substituing:

`\begin{gathered} 130000=P(1+0.05)^(30) \\ 130000=P*(1.05)^(30) \\ 130000=P*(4.322) \\ P=(130000)/(4.322)=30078.667\approx30079 \end{gathered}`

The initial amount to get $130,000 in 30 years is: $30078.7.