Question:
Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
Correct Answer
$6667.5
Solution And Explanation
Solution
Given,
Principal (P) = $5250
Rate of Simple Interest (SI) = 3%
Time (t) = 9 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% × 9
= $5250 ×3/100 × 9
= 5250 × 3 × 9/100
= 15750 × 9/100
= 141750/100
= $1417.5
Thus, Simple Interest = $1417.5
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 + $1417.5
= $6667.5
Thus, Amount to be paid = $6667.5 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) = 9 years
Thus, Amount (A)
= $5250 + ($5250 × 3% × 9)
= $5250 + ($5250 ×3/100 × 9)
= $5250 + (5250 × 3 × 9/100)
= $5250 + (15750 × 9/100)
= $5250 + (141750/100)
= $5250 + $1417.5 = $6667.5
Thus, Amount (A) to be paid = $6667.5 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 9 years
= Simple interest for 1 year × 9
= $157.5 × 9 = $1417.5
Thus, Simple Interest (SI) = $1417.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $1417.5
= $6667.5
Thus, Amount to be paid = $6667.5 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(2) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(3) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(6) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.
(8) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.
(10) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.