Question:
If David borrowed $3400 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3604
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 3%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $3400 × 3% × 2
= $3400 ×3/100 × 2
= 3400 × 3 × 2/100
= 10200 × 2/100
= 20400/100
= $204
Thus, Simple Interest = $204
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 = $3400 + $204
= $3604
Thus, Amount to be paid = $3604 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 = $3400
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 2 years
Thus, Amount (A)
= $3400 + ($3400 × 3% × 2)
= $3400 + ($3400 ×3/100 × 2)
= $3400 + (3400 × 3 × 2/100)
= $3400 + (10200 × 2/100)
= $3400 + (20400/100)
= $3400 + $204 = $3604
Thus, Amount (A) to be paid = $3604 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3400, the simple interest in 1 year
= 3/100 × 3400
= 3 × 3400/100
= 10200/100 = $102
Thus, simple interest for 1 year = $102
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $102 × 2 = $204
Thus, Simple Interest (SI) = $204
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $204
= $3604
Thus, Amount to be paid = $3604 Answer
Similar Questions
(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(2) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.
(3) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(6) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(7) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?
(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?
(9) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?
(10) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?