Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.
Correct Answer
$8732
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5900 ×6/100 × 8
= 5900 × 6 × 8/100
= 35400 × 8/100
= 283200/100
= $2832
Thus, Simple Interest = $2832
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 + $2832
= $8732
Thus, Amount to be paid = $8732 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5900 + ($5900 × 6% × 8)
= $5900 + ($5900 ×6/100 × 8)
= $5900 + (5900 × 6 × 8/100)
= $5900 + (35400 × 8/100)
= $5900 + (283200/100)
= $5900 + $2832 = $8732
Thus, Amount (A) to be paid = $8732 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5900, the simple interest in 1 year
= 6/100 × 5900
= 6 × 5900/100
= 35400/100 = $354
Thus, simple interest for 1 year = $354
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $354 × 8 = $2832
Thus, Simple Interest (SI) = $2832
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $2832
= $8732
Thus, Amount to be paid = $8732 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?
(4) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
(5) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(8) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.