a 5000 loan, taken now with a simple interest rate of 4% per year, will require a total repayment of 5400dllrs. After how many years t will the loan mature?
I = PRT
400 = 5,000 * 0.04 * t
Solve for t.
2 years
Right.
To find out after how many years the loan will mature, we need to use the formula for simple interest:
Simple Interest = Principal × Rate × Time
Given that the principal amount (P) is $5000, the interest rate (R) is 4%, and the total repayment amount is $5400, we can calculate the interest first:
Interest = Total Repayment - Principal
Interest = $5400 - $5000 = $400
Now, we can plug in the values into the simple interest formula to find the time (T):
Interest = Principal × Rate × Time
$400 = $5000 × 0.04 × T
To solve for T, we can rearrange the formula:
T = Interest / (Principal × Rate)
T = $400 / ($5000 × 0.04)
T = $400 / $200
T = 2 years
Therefore, the loan will mature in 2 years.