Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
Correct Answer
$9617
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 7%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 9
= $5900 ×7/100 × 9
= 5900 × 7 × 9/100
= 41300 × 9/100
= 371700/100
= $3717
Thus, Simple Interest = $3717
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 + $3717
= $9617
Thus, Amount to be paid = $9617 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) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 7% × 9)
= $5900 + ($5900 ×7/100 × 9)
= $5900 + (5900 × 7 × 9/100)
= $5900 + (41300 × 9/100)
= $5900 + (371700/100)
= $5900 + $3717 = $9617
Thus, Amount (A) to be paid = $9617 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5900, the simple interest in 1 year
= 7/100 × 5900
= 7 × 5900/100
= 41300/100 = $413
Thus, simple interest for 1 year = $413
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $413 × 9 = $3717
Thus, Simple Interest (SI) = $3717
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $3717
= $9617
Thus, Amount to be paid = $9617 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 Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(3) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?
(7) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 4 years.
(9) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(10) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.