Question:
Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.
Correct Answer
$7020
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 5%
Time (t) = 7 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% × 7
= $5200 ×5/100 × 7
= 5200 × 5 × 7/100
= 26000 × 7/100
= 182000/100
= $1820
Thus, Simple Interest = $1820
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 + $1820
= $7020
Thus, Amount to be paid = $7020 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) = 7 years
Thus, Amount (A)
= $5200 + ($5200 × 5% × 7)
= $5200 + ($5200 ×5/100 × 7)
= $5200 + (5200 × 5 × 7/100)
= $5200 + (26000 × 7/100)
= $5200 + (182000/100)
= $5200 + $1820 = $7020
Thus, Amount (A) to be paid = $7020 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 7 years
= Simple interest for 1 year × 7
= $260 × 7 = $1820
Thus, Simple Interest (SI) = $1820
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $1820
= $7020
Thus, Amount to be paid = $7020 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(2) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?
(4) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.
(8) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 4 years.
(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(10) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?