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) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.
(3) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 4 years.
(6) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(7) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?
(8) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.