Question
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2. Numeric 1 point Ramesh wants to have \( \$ 50,000 \) in an investment account when his son starts college 17 years from now. Assuming that the account pays \( 5.61 \% \) compounded daily, how much should he have in the account now? (Assume that he will not make any additional deposits.) Type your answer...

Ask by May Gonzalez. in the United States
Feb 03,2025

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Answer

Ramesh should invest approximately \$19,313.50 today.

Solution

To determine how much Ramesh should invest today to have \$50,000 in 17 years with an annual interest rate of 5.61% compounded daily, we can use the **Present Value (PV)** formula for compound interest: \[ PV = \frac{FV}{\left(1 + \frac{r}{n}\right)^{nt}} \] Where: - \( FV = \$50,000 \) (Future Value) - \( r = 0.0561 \) (annual interest rate) - \( n = 365 \) (number of compounding periods per year) - \( t = 17 \) (number of years) Plugging in the values: \[ PV = \frac{50,000}{\left(1 + \frac{0.0561}{365}\right)^{365 \times 17}} \] Calculating the denominator: \[ \left(1 + \frac{0.0561}{365}\right)^{6205} \approx 2.5889 \] Thus: \[ PV = \frac{50,000}{2.5889} \approx 19,313.50 \] **Ramesh should invest approximately \$19,313.50 today.**

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To find out how much Ramesh should invest now to reach \( \$ 50,000 \) in 17 years with a daily compounding interest rate of \( 5.61\% \), we can use the formula for present value: \[ PV = \frac{FV}{(1 + r/n)^{nt}} \] Where \( FV \) is the future value (\$50,000), \( r \) is the annual interest rate (0.0561), \( n \) is the number of times interest is compounded per year (365), and \( t \) is the time in years (17). After plugging in the numbers, Ramesh should invest approximately \( \$ 20,331.29 \) now to meet his goal. To ensure the account grows as planned, Ramesh should consider setting reminders for annual check-ins on his investment progress. It’s easy to get distracted by life’s surprises, but keeping an eye on interest rates and investment performance will help him stay on track! Regularly assessing his goals can also inspire potential adjustments for a better future payoff.

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