Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.
Correct Answer
$6572
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5300 ×3/100 × 8
= 5300 × 3 × 8/100
= 15900 × 8/100
= 127200/100
= $1272
Thus, Simple Interest = $1272
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 + $1272
= $6572
Thus, Amount to be paid = $6572 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 3% × 8)
= $5300 + ($5300 ×3/100 × 8)
= $5300 + (5300 × 3 × 8/100)
= $5300 + (15900 × 8/100)
= $5300 + (127200/100)
= $5300 + $1272 = $6572
Thus, Amount (A) to be paid = $6572 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5300, the simple interest in 1 year
= 3/100 × 5300
= 3 × 5300/100
= 15900/100 = $159
Thus, simple interest for 1 year = $159
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $159 × 8 = $1272
Thus, Simple Interest (SI) = $1272
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1272
= $6572
Thus, Amount to be paid = $6572 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.
(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(3) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?
(5) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.
(7) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.
(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(10) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.