Question:
Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
Correct Answer
$6448
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5200 ×3/100 × 8
= 5200 × 3 × 8/100
= 15600 × 8/100
= 124800/100
= $1248
Thus, Simple Interest = $1248
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 + $1248
= $6448
Thus, Amount to be paid = $6448 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 3% × 8)
= $5200 + ($5200 ×3/100 × 8)
= $5200 + (5200 × 3 × 8/100)
= $5200 + (15600 × 8/100)
= $5200 + (124800/100)
= $5200 + $1248 = $6448
Thus, Amount (A) to be paid = $6448 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5200, the simple interest in 1 year
= 3/100 × 5200
= 3 × 5200/100
= 15600/100 = $156
Thus, simple interest for 1 year = $156
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $156 × 8 = $1248
Thus, Simple Interest (SI) = $1248
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $1248
= $6448
Thus, Amount to be paid = $6448 Answer
Similar Questions
(1) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?
(2) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(3) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?
(4) How much loan did Charles borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6490 to clear it?
(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
(6) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(7) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.
(8) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?
(9) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.