Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.
Correct Answer
$10148
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 9%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $5900 × 9% × 8
= $5900 ×9/100 × 8
= 5900 × 9 × 8/100
= 53100 × 8/100
= 424800/100
= $4248
Thus, Simple Interest = $4248
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 = $5900 + $4248
= $10148
Thus, Amount to be paid = $10148 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 = $5900
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5900 + ($5900 × 9% × 8)
= $5900 + ($5900 ×9/100 × 8)
= $5900 + (5900 × 9 × 8/100)
= $5900 + (53100 × 8/100)
= $5900 + (424800/100)
= $5900 + $4248 = $10148
Thus, Amount (A) to be paid = $10148 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5900, the simple interest in 1 year
= 9/100 × 5900
= 9 × 5900/100
= 53100/100 = $531
Thus, simple interest for 1 year = $531
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $531 × 8 = $4248
Thus, Simple Interest (SI) = $4248
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $4248
= $10148
Thus, Amount to be paid = $10148 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(3) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?
(6) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(7) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.
(9) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.