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) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
(2) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.
(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(4) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?
(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
(6) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(8) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?
(9) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?
(10) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.