Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
Correct Answer
$7130
Solution And Explanation
Solution
Given,
Principal (P) = $5750
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) = $5750 × 3% × 8
= $5750 ×3/100 × 8
= 5750 × 3 × 8/100
= 17250 × 8/100
= 138000/100
= $1380
Thus, Simple Interest = $1380
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 + $1380
= $7130
Thus, Amount to be paid = $7130 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 3% × 8)
= $5750 + ($5750 ×3/100 × 8)
= $5750 + (5750 × 3 × 8/100)
= $5750 + (17250 × 8/100)
= $5750 + (138000/100)
= $5750 + $1380 = $7130
Thus, Amount (A) to be paid = $7130 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 $5750, the simple interest in 1 year
= 3/100 × 5750
= 3 × 5750/100
= 17250/100 = $172.5
Thus, simple interest for 1 year = $172.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $172.5 × 8 = $1380
Thus, Simple Interest (SI) = $1380
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $1380
= $7130
Thus, Amount to be paid = $7130 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(3) John had to pay $3584 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?
(6) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.
(8) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.
(9) Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.