question 24 your older sister deposited $2,500 today at an annual interest rate of 6.25%. how much more…

Explanation:

Step1: Use compound - interest formula

The compound - interest formula is $A = P(1 + r)^n$, where $A$ is the future value, $P$ is the principal amount, $r$ is the annual interest rate, and $n$ is the number of years. Your sister's investment: $P_{sister}=2500$, $r_{sister}=0.0625$, $n = 15$. So $A_{sister}=2500\times(1 + 0.0625)^{15}$. Your investment: Let $P_{you}$ be the principal you need to deposit, $r_{you}=0.065$, $n = 15$, and $A_{you}=A_{sister}$. So $A_{you}=P_{you}\times(1 + 0.065)^{15}$. Since $A_{you}=A_{sister}$, we have $P_{you}\times(1 + 0.065)^{15}=2500\times(1 + 0.0625)^{15}$.

Step2: Solve for $P_{you}$

$P_{you}=2500\times\left(\frac{1 + 0.0625}{1+0.065}\right)^{15}$. First, calculate $\frac{1 + 0.0625}{1+0.065}=\frac{1.0625}{1.065}\approx0.99765$. Then $(0.99765)^{15}\approx0.9642$. So $P_{you}=2500\times0.9642 = 2410.5$. The difference $\Delta P=2500 - 2410.5=89.5\approx89.70$.

Answer:

C. $89.70$