Question:
Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.
Correct Answer
$8112
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 8%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 7
= $5200 ×8/100 × 7
= 5200 × 8 × 7/100
= 41600 × 7/100
= 291200/100
= $2912
Thus, Simple Interest = $2912
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 + $2912
= $8112
Thus, Amount to be paid = $8112 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) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5200 + ($5200 × 8% × 7)
= $5200 + ($5200 ×8/100 × 7)
= $5200 + (5200 × 8 × 7/100)
= $5200 + (41600 × 7/100)
= $5200 + (291200/100)
= $5200 + $2912 = $8112
Thus, Amount (A) to be paid = $8112 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5200, the simple interest in 1 year
= 8/100 × 5200
= 8 × 5200/100
= 41600/100 = $416
Thus, simple interest for 1 year = $416
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $416 × 7 = $2912
Thus, Simple Interest (SI) = $2912
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2912
= $8112
Thus, Amount to be paid = $8112 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?
(3) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?
(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?
(5) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(6) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(7) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?
(9) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?