Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.
Correct Answer
$9810
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5450 ×10/100 × 8
= 5450 × 10 × 8/100
= 54500 × 8/100
= 436000/100
= $4360
Thus, Simple Interest = $4360
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 + $4360
= $9810
Thus, Amount to be paid = $9810 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 10% × 8)
= $5450 + ($5450 ×10/100 × 8)
= $5450 + (5450 × 10 × 8/100)
= $5450 + (54500 × 8/100)
= $5450 + (436000/100)
= $5450 + $4360 = $9810
Thus, Amount (A) to be paid = $9810 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5450, the simple interest in 1 year
= 10/100 × 5450
= 10 × 5450/100
= 54500/100 = $545
Thus, simple interest for 1 year = $545
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $545 × 8 = $4360
Thus, Simple Interest (SI) = $4360
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $4360
= $9810
Thus, Amount to be paid = $9810 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.
(2) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.
(5) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 7 years.
(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?
(9) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.