Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.
Correct Answer
$8892
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 7%
Time (t) = 8 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% × 8
= $5700 ×7/100 × 8
= 5700 × 7 × 8/100
= 39900 × 8/100
= 319200/100
= $3192
Thus, Simple Interest = $3192
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 + $3192
= $8892
Thus, Amount to be paid = $8892 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) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 7% × 8)
= $5700 + ($5700 ×7/100 × 8)
= $5700 + (5700 × 7 × 8/100)
= $5700 + (39900 × 8/100)
= $5700 + (319200/100)
= $5700 + $3192 = $8892
Thus, Amount (A) to be paid = $8892 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 8 years
= Simple interest for 1 year × 8
= $399 × 8 = $3192
Thus, Simple Interest (SI) = $3192
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $3192
= $8892
Thus, Amount to be paid = $8892 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(2) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.
(5) What amount does James have to pay after 5 years if he takes a loan of $3000 at 3% simple interest?
(6) How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?
(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.
(8) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.
(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?