Question:
What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
Correct Answer
$4000
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 5%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 5
= $3200 ×5/100 × 5
= 3200 × 5 × 5/100
= 16000 × 5/100
= 80000/100
= $800
Thus, Simple Interest = $800
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 + $800
= $4000
Thus, Amount to be paid = $4000 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) = 5%
And, Time (t) = 5 years
Thus, Amount (A)
= $3200 + ($3200 × 5% × 5)
= $3200 + ($3200 ×5/100 × 5)
= $3200 + (3200 × 5 × 5/100)
= $3200 + (16000 × 5/100)
= $3200 + (80000/100)
= $3200 + $800 = $4000
Thus, Amount (A) to be paid = $4000 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3200, the simple interest in 1 year
= 5/100 × 3200
= 5 × 3200/100
= 16000/100 = $160
Thus, simple interest for 1 year = $160
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $160 × 5 = $800
Thus, Simple Interest (SI) = $800
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $800
= $4000
Thus, Amount to be paid = $4000 Answer
Similar Questions
(1) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?
(2) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.
(5) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(6) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.
(7) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(9) William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.