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) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.
(2) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?
(4) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?
(5) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.
(7) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(8) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?
(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.