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) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?
(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(3) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 7 years.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.
(6) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(7) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(8) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8296 to clear the loan, then find the time period of the loan.
(10) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?