Question:
Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.
Correct Answer
$6510
Solution And Explanation
Solution
Given,
Principal (P) = $5250
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) = $5250 × 3% × 8
= $5250 ×3/100 × 8
= 5250 × 3 × 8/100
= 15750 × 8/100
= 126000/100
= $1260
Thus, Simple Interest = $1260
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 = $5250 + $1260
= $6510
Thus, Amount to be paid = $6510 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 = $5250
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5250 + ($5250 × 3% × 8)
= $5250 + ($5250 ×3/100 × 8)
= $5250 + (5250 × 3 × 8/100)
= $5250 + (15750 × 8/100)
= $5250 + (126000/100)
= $5250 + $1260 = $6510
Thus, Amount (A) to be paid = $6510 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 $5250, the simple interest in 1 year
= 3/100 × 5250
= 3 × 5250/100
= 15750/100 = $157.5
Thus, simple interest for 1 year = $157.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $157.5 × 8 = $1260
Thus, Simple Interest (SI) = $1260
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $1260
= $6510
Thus, Amount to be paid = $6510 Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9238 to clear the loan, then find the time period of the loan.
(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(4) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(7) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?
(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?
(9) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(10) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?