Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
Correct Answer
$8970
Solution And Explanation
Solution
Given,
Principal (P) = $5750
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) = $5750 × 8% × 7
= $5750 ×8/100 × 7
= 5750 × 8 × 7/100
= 46000 × 7/100
= 322000/100
= $3220
Thus, Simple Interest = $3220
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 = $5750 + $3220
= $8970
Thus, Amount to be paid = $8970 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 = $5750
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5750 + ($5750 × 8% × 7)
= $5750 + ($5750 ×8/100 × 7)
= $5750 + (5750 × 8 × 7/100)
= $5750 + (46000 × 7/100)
= $5750 + (322000/100)
= $5750 + $3220 = $8970
Thus, Amount (A) to be paid = $8970 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 $5750, the simple interest in 1 year
= 8/100 × 5750
= 8 × 5750/100
= 46000/100 = $460
Thus, simple interest for 1 year = $460
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $460 × 7 = $3220
Thus, Simple Interest (SI) = $3220
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $3220
= $8970
Thus, Amount to be paid = $8970 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?
(4) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?
(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?
(7) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.
(8) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
(10) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.