Question:
Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
Correct Answer
$3712
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 4%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 4
= $3200 ×4/100 × 4
= 3200 × 4 × 4/100
= 12800 × 4/100
= 51200/100
= $512
Thus, Simple Interest = $512
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 + $512
= $3712
Thus, Amount to be paid = $3712 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) = 4%
And, Time (t) = 4 years
Thus, Amount (A)
= $3200 + ($3200 × 4% × 4)
= $3200 + ($3200 ×4/100 × 4)
= $3200 + (3200 × 4 × 4/100)
= $3200 + (12800 × 4/100)
= $3200 + (51200/100)
= $3200 + $512 = $3712
Thus, Amount (A) to be paid = $3712 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3200, the simple interest in 1 year
= 4/100 × 3200
= 4 × 3200/100
= 12800/100 = $128
Thus, simple interest for 1 year = $128
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $128 × 4 = $512
Thus, Simple Interest (SI) = $512
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $512
= $3712
Thus, Amount to be paid = $3712 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(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) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
(5) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
(7) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(8) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(9) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?
(10) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.