Question

Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. After c years, Calvin has $658. 80. Makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. After m years, Makayla has $613. 4. What is the approximate difference in the number of years that Calvin and Makayla have their money invested?.

Answer 1

The approximate difference between Calvin and Makayla's number of years of money invested is 2 years.

What is compound interest?

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

$A=P\left(1+\dfrac{r}{t}\right)^{t}$

Here, $A$ is the final amount (principal plus interest amount) on the principal amount of $P$ with the rate of $r$ in the time period of $t$.

Calvin deposits $400 in a savings account and Interest rate is 5 present compounded monthly.

As the final amount Calvin has $658.80 in c years. Thus the monthly compound interest can be given as,

$658.8=400\left(1+\dfrac{5}{12\times100}\right)^{12c}\\\dfrac{658.8}{400}=\left(\dfrac{1205}{1200}\right)^{12c}\\c\cong10\rm years$

Now Makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. The final amount she gets is $613.4 in m years. Thus,

$613.4=300\left(1+\dfrac{6}{12\times100}\right)^{12m}\\\dfrac{613.4}{300}=\left(\dfrac{1206}{1200}\right)^{12m}\\c\cong12\rm years$

Thus, the approximate difference in the number of years that Calvin and Makayla have their money invested is 2 years.

Learn more about the compound interest here;

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