Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.
Correct Answer
$9116
Solution And Explanation
Solution
Given,
Principal (P) = $5300
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) = $5300 × 9% × 8
= $5300 ×9/100 × 8
= 5300 × 9 × 8/100
= 47700 × 8/100
= 381600/100
= $3816
Thus, Simple Interest = $3816
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 = $5300 + $3816
= $9116
Thus, Amount to be paid = $9116 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 = $5300
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 9% × 8)
= $5300 + ($5300 ×9/100 × 8)
= $5300 + (5300 × 9 × 8/100)
= $5300 + (47700 × 8/100)
= $5300 + (381600/100)
= $5300 + $3816 = $9116
Thus, Amount (A) to be paid = $9116 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 $5300, the simple interest in 1 year
= 9/100 × 5300
= 9 × 5300/100
= 47700/100 = $477
Thus, simple interest for 1 year = $477
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $477 × 8 = $3816
Thus, Simple Interest (SI) = $3816
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $3816
= $9116
Thus, Amount to be paid = $9116 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(2) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.
(4) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(5) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(7) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?
(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.
(10) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?