Question

Harriet used her credit card to buy a $779 laptop, which she paid off by making identical monthly payments for two and a half years. Over the six years that she kept the laptop, it cost her an average of $0. 36 of electricity per day. Harriet’s credit card has an APR of 11. 27%, compounded monthly, and she made no other purchases with her credit card until she had paid off the laptop. What percentage of the lifetime cost of the laptop was interest? (Assume that there were two leap years over the period that Harriet kept the laptop, and round all dollar values to the nearest cent. ) a. 7. 03% b. 13. 21% c. 11. 27% d. 6. 97%.

Answer 1

Interest is the charge that is levied on the principal at a fixed percentage. The percentage of interest in the lifetime cost of the laptop is 13.7%.

What is interest?

Interest is the payment that the borrower incurs as a percentage of the principal for borrowing money.

Compound interest refers to the interest calculated on the principal and the interest up to the current interest period. The compound interest can be calculated using the formula:

$\rm Compound\:interest = P(1+ \dfrac{r}{n})^{nt} - P$  , where P is the principal amount, r is the rate of interest, n is the number of times the interest is compounded, and t is the tenure. The total number of period is represented as nt.

The total lifetime cost of the laptop will be the combination of its purchase price, interest, and electricity expense.

Given,

The value of the laptop (P) is $779

The number of years of the loan is 2.5 years.

The APR is 11.27%.

The interest on the laptop will be:

$\rm Compound\:interest = P(1+ \dfrac{r}{n})^{nt} - P\\\\\rm Compound\:interest = \ 779(1+ \dfrac{0.1127}{12})^{(12)(2.5)} - \ 779\\\\\rm Compound\:interest = \ 779(1.0094)^{30} - \ 779\\\\\rm Compound\:interest = \ 779(1.3237) - \ 779\\\\\rm Compound\:interest = \ 1031.167 - \ 779\\\\\rm Compound\:interest = \ 252.167$

The electricity charges for 6 years will be calculated as the product of electricity charges per day and the number of days in 6 years.

Total number of days will be calculated as:

$\rm Total\:number\:of\:days = (365 \times 4) + (366 \times 2)\\\\\rm Total\:number\:of\:days = 2192 \:days$

Therefore electricity charges will be:

$\rm Electricity \:charges = 2192 \times \ 0.36\\\\\rm Electricity \:charges = \ 789.12$

Hence the total lifetime value of the laptop is:

$\rm Total\: lifetime \:value = \ 779 + \ 252.167 + \ 789.12\\\\\rm Total\: lifetime \:value = \ 1830.287$

The percentage of interest in total lifetime value is:

$\rm Percentage\:of\:interest = \dfrac{Interest}{Total\: lifetime \:value}\times 100\\\\\rm Percentage\:of\:interest = \dfrac{252.167}{1830.287}\times 100\\\\\rm Percentage\:of\:interest = 13.7\%$

The difference in answers could be a result of rounding. Therefore the correct option is b.

Learn more about interest here:

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