Questions: You would like to have 800,000 when you retire in 35 years. How much should you invest each quarter if you can earn a rate of 2.7% compounded quarterly? a) How much should you deposit each quarter? Round your answer to the nearest cent. b) How much total money will you put into the account? Round your answer to the nearest cent. c) How much total interest will you earn? Round your answer to the nearest cent.

You would like to have 800,000 when you retire in 35 years. How much should you invest each quarter if you can earn a rate of 2.7% compounded quarterly? a) How much should you deposit each quarter? Round your answer to the nearest cent. b) How much total money will you put into the account? Round your answer to the nearest cent. c) How much total interest will you earn? Round your answer to the nearest cent.
Transcript text: You would like to have $\$ 800,000$ when you retire in 35 years. How much should you invest each quarter if you can earn a rate of $2.7 \%$ compounded quarterly? a) How much should you deposit each quarter? Round your answer to the nearest cent. $\$$ $\square$ b) How much total money will you put into the account? Round your answer to the nearest cent. $\$$ $\square$ c) How much total interest will you earn? Round your answer to the nearest cent. \$ $\square$ Question Help: Message instructor
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Solution

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Solution Steps

Step 1: Calculate the Periodic Deposit (PMT)

To achieve a future value of $800000 with an annual interest rate of 2.7% compounded 4 times per year for 35 years, the periodic deposit (PMT) is calculated using the formula: $$PMT = \frac{FV}{\frac{(1 + \frac{r}{n})^{n*t} - 1}{\frac{r}{n}}}$$ Substituting the given values, we get: $$PMT = rac{800000}{ rac{(1 + rac{0.027}{4})^{140} - 1}{ rac{0.027}{4}}} = 3451.23$$

Step 2: Calculate the Total Amount Deposited

The total amount deposited over the period is calculated as: $$Total\ Deposited = PMT * n * t$$ Substituting the values, we get: $$Total\ Deposited = 3451.23 * 4 * 35 = 483172.86$$

Step 3: Calculate the Total Interest Earned

The total interest earned over the period is calculated as: $$Total\ Interest = FV - (PMT * n * t)$$ Substituting the values, we get: $$Total\ Interest = 800000 - (3451.23 * 4 * 35) = 316827.14$$

Final Answer:

The periodic deposit required is $3451.23. The total amount deposited over the period is $483172.86. The total interest earned over the period is $316827.14.

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