Question:
Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.
Correct Answer
$7450
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 7%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5000 × 7% × 7
= $5000 ×7/100 × 7
= 5000 × 7 × 7/100
= 35000 × 7/100
= 245000/100
= $2450
Thus, Simple Interest = $2450
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $2450
= $7450
Thus, Amount to be paid = $7450 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5000
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5000 + ($5000 × 7% × 7)
= $5000 + ($5000 ×7/100 × 7)
= $5000 + (5000 × 7 × 7/100)
= $5000 + (35000 × 7/100)
= $5000 + (245000/100)
= $5000 + $2450 = $7450
Thus, Amount (A) to be paid = $7450 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5000, the simple interest in 1 year
= 7/100 × 5000
= 7 × 5000/100
= 35000/100 = $350
Thus, simple interest for 1 year = $350
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $350 × 7 = $2450
Thus, Simple Interest (SI) = $2450
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $2450
= $7450
Thus, Amount to be paid = $7450 Answer
Similar Questions
(1) If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?
(4) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(5) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?
(7) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(8) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(9) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?
(10) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?