Question

Clint invested $6000 in a savings account for 12.5 years. At the end of 12.5 years, his savings account had $8250 in it. If $6000 represents P, the principal amount, which percent represents the annual simple interest rate (r) that Clint earned after the 12.5 year (t) period?

Answer 1

`\bf ~~~~~~ \textit{Simple Interest Earned Amount}\\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\to &\$8250\\ P=\textit{original amount deposited}\to& \$6000\\ r=rate\to r\%\to (r)/(100)\\ t=years\to &12.5 \end{cases} \\\\\\ 8250=6000[1+(r)(12.5)]\implies \cfrac{8250}{6000}=1+12.5r \\\\\\ \cfrac{11}{8}=1+12.5r \implies \cfrac{11}{8}-1=12.5r\implies \cfrac{(11)/(8)-1}{12.5}=r \\\\\\ 0.03=r\implies r\%=003\cdot 100\implies r=\stackrel{\%}{3}`

Answer 2

The balance B at the end of time t is given by
B = P +Prt
8250 = 6000 +6000*r*12.5 . . . . substitute the given information
2250 = 6000*r*12.5 . . . . . . . . . . .subtract 6000
2250/(6000*12.5) = r . . . . . . . . . .divide by the coefficient of r
r = .03 = 3%

Clint earned 3% annual simple interest on his savings.