Question

Another bank is also offering favorable terms, so Van decides to take a loan of $23,000 from this bank. He signs the loan contract at 13.00% compounded daily for four months. Based on a 365-day year, what is the total amount that Van owes the bank at the end of the loan’s term? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.) $24,017.91 $24,858.54 $24,978.63 $25,458.98

Answer 1

Ans. The total amount that Van owes the bank at the end of the loan’s term is A) 24,017.91

Step-by-step explanation:

Hi, first, let´s do what the hint of the problem says. Let´s find the number of days.

`NumberDays=(4)/(12) *365=121.6667 Days`

Then, we have to turn that compounded daily rate to an effective daily rate, that is by dividing the rate by 365.

`EffectiveDaily=(0.13)/(365) =0.000356164`

This means that 13% compounded daily is equal to 0.0356164%

Now, we can use the following equation to find the future value (in 4 months) of this obligation.

`FutureValue=PresentValue(1+r)^(n)`

Where:

r= Effective rate of the loan (in our case, effective daily)

n= days to pay the loan (121.6667 days)

The math to this as follows.

`FutureValue=23,000(1+0.000356164)^(121.6667)`

`FutureValue=24,018.39`

Since I used the whole decimals to find the exact value, my result is close to answer A), therefore, total amount that Van owes the bank at the end of the loan’s term is $24,017.91.

Best of luck