Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
Correct Answer
$7085
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 3%
Time (t) = 10 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) = $5450 × 3% × 10
= $5450 ×3/100 × 10
= 5450 × 3 × 10/100
= 16350 × 10/100
= 163500/100
= $1635
Thus, Simple Interest = $1635
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 = $5450 + $1635
= $7085
Thus, Amount to be paid = $7085 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 = $5450
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 3% × 10)
= $5450 + ($5450 ×3/100 × 10)
= $5450 + (5450 × 3 × 10/100)
= $5450 + (16350 × 10/100)
= $5450 + (163500/100)
= $5450 + $1635 = $7085
Thus, Amount (A) to be paid = $7085 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 $5450, the simple interest in 1 year
= 3/100 × 5450
= 3 × 5450/100
= 16350/100 = $163.5
Thus, simple interest for 1 year = $163.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $163.5 × 10 = $1635
Thus, Simple Interest (SI) = $1635
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $1635
= $7085
Thus, Amount to be paid = $7085 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 $7854 to clear the loan, then find the time period of the loan.
(2) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.
(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.
(5) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?
(10) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.