## Related questions with answers

The total amount of money in a bank account paying compound interest can be determined by the formula $A=P\left(1+\frac{r}{n}\right)^{n t}$, where $P$ is the principal (amount deposited), $r$ is the annual rate of interest expressed as a decimal, $n$ is the number of times the interest is compounded in one year, and $t$ is the time in years. Determine the total amount of money in an account at the end of 4 months if the original sum deposited was $\$ 2550$, the interest rate is $8 \%$, compounded 4 times a year, and no money is deposited or withdrawn.

Solution

VerifiedWe are tasked to solve for the total amount of money $A$ given the following values:

Time in years: $\mathrm{t = 4 \ months = 4 \ \cancel{months }\cdot \frac{1 \ year}{12 \ \cancel{months }} = \frac{1}{3} \ year}$

Principal amount: $P = \$2550$

Interest rate: $r = 8 \% =0.08$

Number of times the interest is compounded in one year: $n = 4$

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