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 David borrowed a sum of $5400 at 7% simple interest for 7 years.
(2) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?
(3) 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.
(4) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?
(5) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
(6) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(7) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.
(9) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?