Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.
Correct Answer
$9718
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 9%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $5650 × 9% × 8
= $5650 ×9/100 × 8
= 5650 × 9 × 8/100
= 50850 × 8/100
= 406800/100
= $4068
Thus, Simple Interest = $4068
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 = $5650 + $4068
= $9718
Thus, Amount to be paid = $9718 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 = $5650
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 9% × 8)
= $5650 + ($5650 ×9/100 × 8)
= $5650 + (5650 × 9 × 8/100)
= $5650 + (50850 × 8/100)
= $5650 + (406800/100)
= $5650 + $4068 = $9718
Thus, Amount (A) to be paid = $9718 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5650, the simple interest in 1 year
= 9/100 × 5650
= 9 × 5650/100
= 50850/100 = $508.5
Thus, simple interest for 1 year = $508.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $508.5 × 8 = $4068
Thus, Simple Interest (SI) = $4068
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $4068
= $9718
Thus, Amount to be paid = $9718 Answer
Similar Questions
(1) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
(2) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(3) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.
(4) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?
(7) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?
(8) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?
(9) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.