Questions: Suppose you want to have 300,000 for retirement in 20 years. Your account earns 8% interest. Round your answers to the nearest cent. a) How much would you need to deposit in the account each month? 509.32

Suppose you want to have 300,000 for retirement in 20 years. Your account earns 8% interest. Round your answers to the nearest cent.
a) How much would you need to deposit in the account each month?
509.32

Transcript text: Suppose you want to have $\$ 300,000$ for retirement in 20 years. Your account earns $8 \%$ interest. Round your answers to the nearest cent. a) How much would you need to deposit in the account each month? \$ 509.32

Solution

Solution Steps

Step 1: Calculate the Monthly Deposit

To reach a future value of $300000 in 20 years with an annual interest rate of 8%, the monthly deposit (PMT) is calculated using the formula: $$ PMT = \frac{P}{\left( \frac{(1 + r/12)^{n} - 1}{r/12} \right)} $$ Substituting the given values, we get: $$ PMT = rac{300000}{\left( rac{(1 + 0.08/12)^{240} - 1}{0.08/12} ight)} = 509.32 $$

Step 2: Calculate the Total Interest Earned

The total amount deposited over the period is $122236.8, and the total interest earned is the difference between the future value (P) and the total amount deposited, which is $300000 - $122236.8 = $177763.2.