You have just taken out a $2,650 loan from your local bank. You paid off the loan in 1 year by making 12 monthly payments with a total interest charge of $300.00. Determine, from the information given, the annual percentage rate (APR). Round your answer to the nearest hundredth of a percent.
The interest generated in one year = $300
Amount borrowed = $2,650
Interest rate: 300/2650 x 100
Interest rate = 11.32% annually
Answer:
20.33%
Step-by-step explanation:
Principal = $2650
Total Interest = $300
Total amount = 42650+$300=$2950
Since we are given that You paid off the loan in 1 year by making 12 monthly payments
So, monthly payment = \(\frac{2950}{12} =245.833\)
Formula of monthly payment = \(\text{Monthly payment }= \frac{Principal \times \frac{i}{12}}{1-(1+\frac{i}{12})^{-12}}\)
where i is the rate of interest in decimals
To find i substitute the values
\(245.833= \frac{2650 \times \frac{i}{12}}{1-(1+\frac{i}{12})^{-12}}\)
using calculator
\(i=0.2033\)
So, rate of interest in percent = \(0.2033 \times 100 = 20.33\%\)
Thus the annual percentage rate (APR) is 20.33%