Question

Use the following compound interest formula to complete the problem. a = p (1 startfraction r over n endfraction) superscript n superscript t victor has a credit card with an apr of 13.66%, compounded monthly. he currently owes a balance of $1,349.34. assuming that victor makes no purchases or payments, how much will he owe after one year, to the nearest cent? a. $1,349.34 b. $1,533.66 c. $1,545.65 d. $1,364.70

Answer 1

The final amount that Victor will owe after one year, to the nearest cent is given by: Option C: $545.65

How to find the compound interest?

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

$a = p(1 + \dfrac{r}{n})^{nt}$

For this case, we're provided that:

The interest rate is r = 13.66% = 13.66/100 = 0.1366 (converted percent to decimal)

It is compounding monthly, thus, 12 times a year, or n = 12

The initial amount that the credit card of Victor has = p = $1349.34

Time for which interest was compounded = a year = 1 = t

Thus, the final amount that Victor will owe after one year to the nearest cent is calculated as;

$a = p(1 + \dfrac{r}{n})^{nt}\\\\a = 1349.34(1 + \dfrac{0.1366}{12})^{12\times 1}\\\\a = 1349.34(1.01138)^{12} \approx 1245.65 \: \rm (in \: dollars)$

Thus, the final amount that Victor will owe after one year, to the nearest cent is given by: Option C: $545.65

Learn more about compound interest here:

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