Question:
Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
Correct Answer
$7280
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5200 × 5% × 8
= $5200 ×5/100 × 8
= 5200 × 5 × 8/100
= 26000 × 8/100
= 208000/100
= $2080
Thus, Simple Interest = $2080
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 = $5200 + $2080
= $7280
Thus, Amount to be paid = $7280 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 = $5200
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 5% × 8)
= $5200 + ($5200 ×5/100 × 8)
= $5200 + (5200 × 5 × 8/100)
= $5200 + (26000 × 8/100)
= $5200 + (208000/100)
= $5200 + $2080 = $7280
Thus, Amount (A) to be paid = $7280 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5200, the simple interest in 1 year
= 5/100 × 5200
= 5 × 5200/100
= 26000/100 = $260
Thus, simple interest for 1 year = $260
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $260 × 8 = $2080
Thus, Simple Interest (SI) = $2080
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2080
= $7280
Thus, Amount to be paid = $7280 Answer
Similar Questions
(1) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?
(2) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?
(4) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?
(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?
(7) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.
(10) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?