Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.
Correct Answer
$8268
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 8%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 7
= $5300 ×8/100 × 7
= 5300 × 8 × 7/100
= 42400 × 7/100
= 296800/100
= $2968
Thus, Simple Interest = $2968
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 + $2968
= $8268
Thus, Amount to be paid = $8268 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) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 8% × 7)
= $5300 + ($5300 ×8/100 × 7)
= $5300 + (5300 × 8 × 7/100)
= $5300 + (42400 × 7/100)
= $5300 + (296800/100)
= $5300 + $2968 = $8268
Thus, Amount (A) to be paid = $8268 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5300, the simple interest in 1 year
= 8/100 × 5300
= 8 × 5300/100
= 42400/100 = $424
Thus, simple interest for 1 year = $424
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $424 × 7 = $2968
Thus, Simple Interest (SI) = $2968
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2968
= $8268
Thus, Amount to be paid = $8268 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(2) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?
(3) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.
(7) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(9) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?