ashley invested $59,000 in an account paying an interest rate of $3\\frac{1}{8}\\%$ compounded daily. fwam…

ashley invested $59,000 in an account paying an interest rate of $3\\frac{1}{8}\\%$ compounded daily. fwam invested $59,000 in an account paying an interest rate of $2\\frac{3}{4}\\%$ compounded annually. after 15 years, how much more money would ashley have in her account than fwam, to the nearest dollar?

ashley invested $59,000 in an account paying an interest rate of $3\\frac{1}{8}\\%$ compounded daily. fwam invested $59,000 in an account paying an interest rate of $2\\frac{3}{4}\\%$ compounded annually. after 15 years, how much more money would ashley have in her account than fwam, to the nearest dollar?

Answer

Explanation:

Step1: Calculate Ashley's amount

The compound - interest formula for compounding (n) times a year is (A = P(1+\frac{r}{n})^{nt}). For Ashley: (P = 59000), (r=3\frac{1}{8}%=0.03125), (n = 365) (compounded daily), (t = 15). [ \begin{align*} A_{Ashley}&=59000\left(1+\frac{0.03125}{365}\right)^{365\times15}\ &=59000\left(1+\frac{0.03125}{365}\right)^{5475}\ \end{align*} ] Using a calculator, (A_{Ashley}\approx59000\times1.6077 = 94854.3)

Step2: Calculate Fwam's amount

The compound - interest formula for compounding annually ((n = 1)) is (A=P(1 + r)^{t}). For Fwam: (P = 59000), (r=2\frac{3}{4}%=0.0275), (t = 15), (n = 1) [ \begin{align*} A_{Fwam}&=59000(1 + 0.0275)^{15}\ &=59000\times(1.0275)^{15}\ \end{align*} ] Using a calculator, ((1.0275)^{15}\approx1.5), (A_{Fwam}=59000\times1.5=88500)

Step3: Find the difference

(A_{Ashley}-A_{Fwam}=94854.3 - 88500=6354.3\approx6354)

Answer:

(6354)