Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.
Correct Answer
$8378
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 6%
Time (t) = 7 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% × 7
= $5900 ×6/100 × 7
= 5900 × 6 × 7/100
= 35400 × 7/100
= 247800/100
= $2478
Thus, Simple Interest = $2478
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 + $2478
= $8378
Thus, Amount to be paid = $8378 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) = 7 years
Thus, Amount (A)
= $5900 + ($5900 × 6% × 7)
= $5900 + ($5900 ×6/100 × 7)
= $5900 + (5900 × 6 × 7/100)
= $5900 + (35400 × 7/100)
= $5900 + (247800/100)
= $5900 + $2478 = $8378
Thus, Amount (A) to be paid = $8378 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 7 years
= Simple interest for 1 year × 7
= $354 × 7 = $2478
Thus, Simple Interest (SI) = $2478
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $2478
= $8378
Thus, Amount to be paid = $8378 Answer
Similar Questions
(1) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?
(3) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.
(4) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.
(6) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(7) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(8) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.