Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
Correct Answer
$9676
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 8
= $5900 ×8/100 × 8
= 5900 × 8 × 8/100
= 47200 × 8/100
= 377600/100
= $3776
Thus, Simple Interest = $3776
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 + $3776
= $9676
Thus, Amount to be paid = $9676 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5900 + ($5900 × 8% × 8)
= $5900 + ($5900 ×8/100 × 8)
= $5900 + (5900 × 8 × 8/100)
= $5900 + (47200 × 8/100)
= $5900 + (377600/100)
= $5900 + $3776 = $9676
Thus, Amount (A) to be paid = $9676 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5900, the simple interest in 1 year
= 8/100 × 5900
= 8 × 5900/100
= 47200/100 = $472
Thus, simple interest for 1 year = $472
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $472 × 8 = $3776
Thus, Simple Interest (SI) = $3776
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $3776
= $9676
Thus, Amount to be paid = $9676 Answer
Similar Questions
(1) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?
(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?
(3) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(4) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.
(5) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.
(7) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.
(9) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(10) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.