Question:
What amount does John have to pay after 5 years if he takes a loan of $3200 at 9% simple interest?
Correct Answer
$4640
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 9%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $3200 × 9% × 5
= $3200 ×9/100 × 5
= 3200 × 9 × 5/100
= 28800 × 5/100
= 144000/100
= $1440
Thus, Simple Interest = $1440
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 = $3200 + $1440
= $4640
Thus, Amount to be paid = $4640 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 = $3200
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 5 years
Thus, Amount (A)
= $3200 + ($3200 × 9% × 5)
= $3200 + ($3200 ×9/100 × 5)
= $3200 + (3200 × 9 × 5/100)
= $3200 + (28800 × 5/100)
= $3200 + (144000/100)
= $3200 + $1440 = $4640
Thus, Amount (A) to be paid = $4640 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3200, the simple interest in 1 year
= 9/100 × 3200
= 9 × 3200/100
= 28800/100 = $288
Thus, simple interest for 1 year = $288
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $288 × 5 = $1440
Thus, Simple Interest (SI) = $1440
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $1440
= $4640
Thus, Amount to be paid = $4640 Answer
Similar Questions
(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.
(2) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
(5) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(6) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.
(7) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(8) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 7 years.
(10) How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?