Question

If a savings account of $10,000 is compounded semi-annually at 19.82% annual interest, how much will the account be worth in 54 months? Round your answer tothe nearest cent, if necessary. Note: 365 days in a year and 30 days in a month.

Answer 1

Using the compound interest formula:

`A=P(1+(r)/(n))^(nt)`

Where:

A = Amount

P = Principal

r = interest rate

n = Number of times the interest is compounded per year

t = time

so:

`\begin{gathered} r=0.1982 \\ P=10000 \\ n=2 \\ t=54_{\text{ }}weeks*(1year)/(52weeks)=(27)/(26) \end{gathered}`
`\begin{gathered} A=10000(1+(0.1982)/(2))^{2\cdot(27)/(26)} \\ A\approx12168.33 \end{gathered}`