Suppose that a loan of $6,500 is given at an interest rate of 7% compounded each year assume that no payments are made on the loan find the amount owed at the end of one year
The formula to calculate the amount owed at the end of the year for a loan with compound interest and no payments made is a = P(1 + r/n)^(nt). In this case, as the loan is compounded each year, n = 1.
Where:
P = Principal amount (the initial amount of money),
r = annual interest rate (in decimal),
t = time in years,
n = number of times the interest is compounded in a year.
So in our case:
P = $6,500
r = 7/100 = 0.07
t = 1 year
n = 1 (compounded annually)
Plug these values into the formula:
a = $6,500(1 + 0.07/1)^(1*1)
a = $6,950
So, by the end of one year, $6,950 would be owed.
To find the amount owed at the end of one year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount owed at the end of one year
P = the principal amount (loan amount) = $6,500
r = annual interest rate (in decimal form) = 7% = 0.07
n = number of times interest is compounded per year = 1 (compounded annually)
t = number of years = 1
Plugging in these values into the formula, we have:
A = 6,500(1 + 0.07/1)^(1*1)
A = 6,500(1.07)^1
A = 6,500 * 1.07
A = $6,955
Therefore, the amount owed at the end of one year will be $6,955.