Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.
Correct Answer
$6148
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 2%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 8
= $5300 ×2/100 × 8
= 5300 × 2 × 8/100
= 10600 × 8/100
= 84800/100
= $848
Thus, Simple Interest = $848
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 + $848
= $6148
Thus, Amount to be paid = $6148 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) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 2% × 8)
= $5300 + ($5300 ×2/100 × 8)
= $5300 + (5300 × 2 × 8/100)
= $5300 + (10600 × 8/100)
= $5300 + (84800/100)
= $5300 + $848 = $6148
Thus, Amount (A) to be paid = $6148 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5300, the simple interest in 1 year
= 2/100 × 5300
= 2 × 5300/100
= 10600/100 = $106
Thus, simple interest for 1 year = $106
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $106 × 8 = $848
Thus, Simple Interest (SI) = $848
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $848
= $6148
Thus, Amount to be paid = $6148 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $10498 to clear the loan, then find the time period of the loan.
(2) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(5) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?
(7) Paul had to pay $5123 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?