Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.
Correct Answer
$8260
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5900 ×5/100 × 8
= 5900 × 5 × 8/100
= 29500 × 8/100
= 236000/100
= $2360
Thus, Simple Interest = $2360
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 + $2360
= $8260
Thus, Amount to be paid = $8260 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5900 + ($5900 × 5% × 8)
= $5900 + ($5900 ×5/100 × 8)
= $5900 + (5900 × 5 × 8/100)
= $5900 + (29500 × 8/100)
= $5900 + (236000/100)
= $5900 + $2360 = $8260
Thus, Amount (A) to be paid = $8260 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5900, the simple interest in 1 year
= 5/100 × 5900
= 5 × 5900/100
= 29500/100 = $295
Thus, simple interest for 1 year = $295
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $295 × 8 = $2360
Thus, Simple Interest (SI) = $2360
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $2360
= $8260
Thus, Amount to be paid = $8260 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(2) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.
(4) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.
(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?
(7) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.