Questions: Luis has 160,000 in his retirement account at his present company. Because he is assuming a position with another company, Luis is planning to roll over his assets to a new account. Luis also plans to put 3500 / quarter into the new account until his retirement 25 years from now. If the new account earns interest at the rate of 9% / year compounded quarterly, how much will Luis have in his account at the time of his retirement? Hint: Use the compound interest formula and the annuity formula. (Round your answer to the nearest cent.)

Luis has 160,000 in his retirement account at his present company. Because he is assuming a position with another company, Luis is planning to roll over his assets to a new account. Luis also plans to put 3500 / quarter into the new account until his retirement 25 years from now. If the new account earns interest at the rate of 9% / year compounded quarterly, how much will Luis have in his account at the time of his retirement? Hint: Use the compound interest formula and the annuity formula. (Round your answer to the nearest cent.)
Transcript text: 7. [-/2 Points] DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Luis has $\$ 160,000$ in his retirement account at his present company. Because he is assuming a position with another company, Luis is planning to roll over his assets to a new account. Luis also plans to put $\$ 3500 / q u a r t e r$ into the new account until his retirement 25 years from now. If the new account earns interest at the rate of $9 \% /$ year compounded quarterly, how much will Luis have in his account at the time of his retirement? Hint: Use the compound interest formula and the annuity formula. (Round your answer to the nearest cent.) \$
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Solution

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Solution Steps

Step 1: Calculate the future value of the initial lump sum investment

Using the formula $FV_{\text{lump sum}} = P(1 + \frac{r}{n})^{nt}$, where $P = 160000$, $r = 0.09$, $n = 4$, and $t = 25$, we find the future value of the initial investment to be $1480647.41$.

Step 2: Calculate the future value of the regular quarterly contributions

Using the formula $FV_{\text{annuity}} = C \left( \frac{(1 + \frac{r}{n})^{nt} - 1}{\frac{r}{n}} \right)$, where $C = 3500$, $r = 0.09$, $n = 4$, and $t = 25$, we find the future value of the regular contributions to be $1283962.76$.

Step 3: Calculate the total amount in the retirement account at the time of retirement

The total amount in the retirement account at the time of retirement, which is the sum of the future value of the initial lump sum investment and the future value of the regular contributions, is $2764610.17$.

Final Answer:

The total future value of the retirement account, considering both the initial lump sum investment and the regular quarterly contributions, is $2764610.17.

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