rahul invested $53,000 in an account paying a...
rahul invested $53,000 in an account paying an interest rate of 2 7/8% compounded annually. layla invested $53,000 in an account paying an interest rate of 2 1/4% compounded continuously. after 7 years, how much more money would rahul have in his account than layla, to the nearest dollar?
Answer
# 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
$A_{Rahul}-A_{Layla}=64170.81 - 62030.14=2140.67\approx104$.