Question:
Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
Correct Answer
$10600
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 10%
Time (t) = 10 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% × 10
= $5300 ×10/100 × 10
= 5300 × 10 × 10/100
= 53000 × 10/100
= 530000/100
= $5300
Thus, Simple Interest = $5300
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 + $5300
= $10600
Thus, Amount to be paid = $10600 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) = 10 years
Thus, Amount (A)
= $5300 + ($5300 × 10% × 10)
= $5300 + ($5300 ×10/100 × 10)
= $5300 + (5300 × 10 × 10/100)
= $5300 + (53000 × 10/100)
= $5300 + (530000/100)
= $5300 + $5300 = $10600
Thus, Amount (A) to be paid = $10600 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 10 years
= Simple interest for 1 year × 10
= $530 × 10 = $5300
Thus, Simple Interest (SI) = $5300
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $5300
= $10600
Thus, Amount to be paid = $10600 Answer
Similar Questions
(1) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.
(3) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.
(4) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.
(6) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?
(7) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(8) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?