Question:
What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 5% simple interest?
Correct Answer
$3740
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 5%
Time (t) = 2 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) = $3400 × 5% × 2
= $3400 ×5/100 × 2
= 3400 × 5 × 2/100
= 17000 × 2/100
= 34000/100
= $340
Thus, Simple Interest = $340
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 + $340
= $3740
Thus, Amount to be paid = $3740 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) = 5%
And, Time (t) = 2 years
Thus, Amount (A)
= $3400 + ($3400 × 5% × 2)
= $3400 + ($3400 ×5/100 × 2)
= $3400 + (3400 × 5 × 2/100)
= $3400 + (17000 × 2/100)
= $3400 + (34000/100)
= $3400 + $340 = $3740
Thus, Amount (A) to be paid = $3740 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 $3400, the simple interest in 1 year
= 5/100 × 3400
= 5 × 3400/100
= 17000/100 = $170
Thus, simple interest for 1 year = $170
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $170 × 2 = $340
Thus, Simple Interest (SI) = $340
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $340
= $3740
Thus, Amount to be paid = $3740 Answer
Similar Questions
(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 4 years.
(2) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
(3) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?
(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(8) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.
(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.