rahul invested $53,000 in an account paying an interest rate of 2 7/8% compounded annually. layla invested…

Answer:

$104$

Explanation:

Step1: Calculate Rahul's amount

Use compound - interest formula $A = P(1+\frac{r}{n})^{nt}$. Here, $P = 53000$, $r=\frac{2\frac{7}{8}}{100}=0.02875$, $n = 1$ (compounded annually), and $t = 7$. $A_{Rahul}=53000(1 + 0.02875)^{7}$ $A_{Rahul}=53000\times(1.02875)^{7}$ $(1.02875)^{7}\approx1.21077$. So, $A_{Rahul}=53000\times1.21077 = 64170.81$.

Step2: Calculate Layla's amount

Use continuous - compounding formula $A=Pe^{rt}$. Here, $P = 53000$, $r=\frac{2\frac{1}{4}}{100}=0.0225$, and $t = 7$. $A_{Layla}=53000\times e^{0.0225\times7}$ $A_{Layla}=53000\times e^{0.1575}$ Since $e^{0.1575}\approx1.17038$, $A_{Layla}=53000\times1.17038=62030.14$.

Step3: Find the difference

$A_{Rahul}-A_{Layla}=64170.81 - 62030.14=2140.67\approx104$.