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) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?
(2) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(3) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(4) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(5) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
(6) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?
(9) 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.
(10) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.