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) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.
(2) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(3) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(4) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(6) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 4 years.
(8) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 4 years.
(10) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?