A man collected $28500 on a loan of $25000 he made 4 years ago. If he charged simple interest, what was the yearly interest rate?
The simple interest formula is
Final amount, A
= P(1+nr)
where P is the principal, n=number of periods (years), and r is the interest rate per annum (5% would be written as 0.05).
Substituting the given values,
28500=25000(1+4r)
Solve for r and convert to percent.
To find the yearly interest rate, you can use the formula for simple interest:
Simple Interest = Principal * Rate * Time
In this problem, the principal is $25000, the interest collected is $28500, and the time is 4 years. Plugging these values into the formula, we get:
28500 = 25000 * Rate * 4
Dividing both sides of the equation by (25000 * 4):
28500 / (25000 * 4) = Rate
Rate = 0.285 or 28.5%
Therefore, the yearly interest rate on the loan is 28.5%.
To find the yearly interest rate, we can start by calculating the total interest earned over the 4-year period.
Step 1: Calculate the interest earned.
Interest = Total amount collected - Principal amount
Interest = $28500 - $25000
Interest = $3500
Step 2: Calculate the yearly interest rate.
Yearly Interest Rate = (Interest / Principal) x (1 / Number of years)
Yearly Interest Rate = ($3500 / $25000) x (1 / 4)
Let's calculate the value of the expression: ($3500 / $25000) x (1 / 4)
Step 3: Simplify the expression.
($3500 / $25000) x (1 / 4) = 0.14 x 0.25
Step 4: Calculate the yearly interest rate.
0.14 x 0.25 = 0.035
Step 5: Convert to a percentage.
0.035 x 100 = 3.5%
Therefore, the yearly interest rate for the loan is 3.5%.