Question:
Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
Correct Answer
$9690
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 7%
Time (t) = 10 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) = $5700 × 7% × 10
= $5700 ×7/100 × 10
= 5700 × 7 × 10/100
= 39900 × 10/100
= 399000/100
= $3990
Thus, Simple Interest = $3990
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 = $5700 + $3990
= $9690
Thus, Amount to be paid = $9690 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 = $5700
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5700 + ($5700 × 7% × 10)
= $5700 + ($5700 ×7/100 × 10)
= $5700 + (5700 × 7 × 10/100)
= $5700 + (39900 × 10/100)
= $5700 + (399000/100)
= $5700 + $3990 = $9690
Thus, Amount (A) to be paid = $9690 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 $5700, the simple interest in 1 year
= 7/100 × 5700
= 7 × 5700/100
= 39900/100 = $399
Thus, simple interest for 1 year = $399
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $399 × 10 = $3990
Thus, Simple Interest (SI) = $3990
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $3990
= $9690
Thus, Amount to be paid = $9690 Answer
Similar Questions
(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.
(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(4) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 8 years.
(6) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.
(7) If Anthony paid $4644 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.
(9) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?