Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.
Correct Answer
$9540
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5300 ×10/100 × 8
= 5300 × 10 × 8/100
= 53000 × 8/100
= 424000/100
= $4240
Thus, Simple Interest = $4240
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 + $4240
= $9540
Thus, Amount to be paid = $9540 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 10% × 8)
= $5300 + ($5300 ×10/100 × 8)
= $5300 + (5300 × 10 × 8/100)
= $5300 + (53000 × 8/100)
= $5300 + (424000/100)
= $5300 + $4240 = $9540
Thus, Amount (A) to be paid = $9540 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5300, the simple interest in 1 year
= 10/100 × 5300
= 10 × 5300/100
= 53000/100 = $530
Thus, simple interest for 1 year = $530
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $530 × 8 = $4240
Thus, Simple Interest (SI) = $4240
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $4240
= $9540
Thus, Amount to be paid = $9540 Answer
Similar Questions
(1) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.
(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
(3) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?
(4) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.
(5) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8344 to clear the loan, then find the time period of the loan.
(6) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(9) If Karen borrowed $3950 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.