a) The total interest paid is $13,750.
b) It takes about 10 years to repay the loan.
How do we solve the problems?
a) To find out how long it takes to repay the loan, we shall calculate the total interest using the formula:
Total Interest (T.I) = Total Cost (TC) − Principal (P)
Given:
Principal = $25,000
Total Cost = $38,750
Total Interest (T.I) = $38,750 - $25,000 = $13,750
b) We find out how long it takes to repay the loan using the simple interest formula:
Simple Interest (S.I) = Principal (P) × Rate (R) ×Time (T)
Given:
P = $38,750
R = 5.5% (0.055 in decimal)
S.I (or T.I) = $13,750
We shall rearrange the formula to solve for time:
T = S.I / P × R
Placing the values into the formula:
T = $13,750 / $25,000 * 0.055
T = 10 years
Hence, the total interest paid is $13,750, and it will take about 10 years to repay the loan.