A loan of $8,532 was repaid at the end of 12 months. What size repayment check (principal and interest) was written, if a 9.5% annual rate of interest was charged?
AMT = 1.095 * $8,532 =
To calculate the size of the repayment check (principal and interest), we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount after interest has been applied
P = the principal amount (initial loan amount)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount is $8,532 and the annual interest rate is 9.5% (0.095 as a decimal). We also know that the loan was repaid at the end of 12 months, so the time (t) is 1 year.
However, we don't know the compounding frequency (n). This information is needed to calculate the interest accurately. Compounding frequency refers to how often interest is added to the loan balance. It could be monthly, quarterly, semi-annually, or annually.
Once we know the compounding frequency, we can use the formula to calculate the total amount owed at the end of the year, which will be the size of the repayment check.