QuestionJuly 19, 2025

Parents wish to have 130,000 available for a child's education . If the child is now 6 years old, how much money must be set aside at 7% compounded I semiannually to meet their financial goal when the child is 18? (i) Click the icon to view some finance formulas. The amount that should be set aside is square (Round up to the nearest dollar.)

Parents wish to have 130,000 available for a child's education . If the child is now 6 years old, how much money must be set aside at 7% compounded I semiannually to meet their financial goal when the child is 18? (i) Click the icon to view some finance formulas. The amount that should be set aside is square (Round up to the nearest dollar.)
Parents wish to have 130,000 available for a child's education . If the child is now 6 years old, how much money must
be set aside at 7%  compounded I semiannually to meet their financial goal when the child is 18?
(i) Click the icon to view some finance formulas.
The amount that should be set aside is
 square 
(Round up to the nearest dollar.)

Solution
4.5(119 votes)

Answer

57,741 Explanation 1. Identify the Formula Use the future value formula for compound interest: **FV = PV \left(1 + \frac{r}{n}\right)^{nt}**, where FV is the future value, PV is the present value, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years. 2. Set Known Values FV = 130,000, r = 0.07, n = 2, t = 12 (since the child is 6 now and will be 18). 3. Rearrange the Formula to Solve for Present Value (PV) PV = \frac{FV}{\left(1 + \frac{r}{n}\right)^{nt}} 4. Calculate Present Value PV = \frac{130,000}{\left(1 + \frac{0.07}{2}\right)^{2 \times 12}} = \frac{130,000}{\left(1.035\right)^{24}} 5. Compute the Result PV \approx \frac{130,000}{2.25219} \approx 57,740.79 6. Round Up Round up to the nearest dollar: 57,741.

Explanation

1. Identify the Formula<br /> Use the future value formula for compound interest: **$FV = PV \left(1 + \frac{r}{n}\right)^{nt}$**, where $FV$ is the future value, $PV$ is the present value, $r$ is the annual interest rate, $n$ is the number of compounding periods per year, and $t$ is the time in years.<br /><br />2. Set Known Values<br /> $FV = 130,000$, $r = 0.07$, $n = 2$, $t = 12$ (since the child is 6 now and will be 18).<br /><br />3. Rearrange the Formula to Solve for Present Value ($PV$)<br /> $PV = \frac{FV}{\left(1 + \frac{r}{n}\right)^{nt}}$<br /><br />4. Calculate Present Value<br /> $PV = \frac{130,000}{\left(1 + \frac{0.07}{2}\right)^{2 \times 12}} = \frac{130,000}{\left(1.035\right)^{24}}$<br /><br />5. Compute the Result<br /> $PV \approx \frac{130,000}{2.25219} \approx 57,740.79$<br /><br />6. Round Up<br /> Round up to the nearest dollar: $57,741$.
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