Question:
Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.
Correct Answer
$3872
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 7%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 3
= $3200 ×7/100 × 3
= 3200 × 7 × 3/100
= 22400 × 3/100
= 67200/100
= $672
Thus, Simple Interest = $672
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 + $672
= $3872
Thus, Amount to be paid = $3872 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) = 7%
And, Time (t) = 3 years
Thus, Amount (A)
= $3200 + ($3200 × 7% × 3)
= $3200 + ($3200 ×7/100 × 3)
= $3200 + (3200 × 7 × 3/100)
= $3200 + (22400 × 3/100)
= $3200 + (67200/100)
= $3200 + $672 = $3872
Thus, Amount (A) to be paid = $3872 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3200, the simple interest in 1 year
= 7/100 × 3200
= 7 × 3200/100
= 22400/100 = $224
Thus, simple interest for 1 year = $224
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $224 × 3 = $672
Thus, Simple Interest (SI) = $672
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $672
= $3872
Thus, Amount to be paid = $3872 Answer
Similar Questions
(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?
(2) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.
(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?
(5) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.
(6) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(7) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?
(8) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(9) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?
(10) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.