Question:
Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
Correct Answer
$7670
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 3%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 10
= $5900 ×3/100 × 10
= 5900 × 3 × 10/100
= 17700 × 10/100
= 177000/100
= $1770
Thus, Simple Interest = $1770
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 + $1770
= $7670
Thus, Amount to be paid = $7670 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) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5900 + ($5900 × 3% × 10)
= $5900 + ($5900 ×3/100 × 10)
= $5900 + (5900 × 3 × 10/100)
= $5900 + (17700 × 10/100)
= $5900 + (177000/100)
= $5900 + $1770 = $7670
Thus, Amount (A) to be paid = $7670 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5900, the simple interest in 1 year
= 3/100 × 5900
= 3 × 5900/100
= 17700/100 = $177
Thus, simple interest for 1 year = $177
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $177 × 10 = $1770
Thus, Simple Interest (SI) = $1770
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $1770
= $7670
Thus, Amount to be paid = $7670 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?
(3) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.
(4) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(5) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(6) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(7) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.
(9) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.