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) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(2) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.
(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?
(5) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(7) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 7 years.