Question:
What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?
Correct Answer
$3920
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 6%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $3500 × 6% × 2
= $3500 ×6/100 × 2
= 3500 × 6 × 2/100
= 21000 × 2/100
= 42000/100
= $420
Thus, Simple Interest = $420
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 = $3500 + $420
= $3920
Thus, Amount to be paid = $3920 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 = $3500
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 2 years
Thus, Amount (A)
= $3500 + ($3500 × 6% × 2)
= $3500 + ($3500 ×6/100 × 2)
= $3500 + (3500 × 6 × 2/100)
= $3500 + (21000 × 2/100)
= $3500 + (42000/100)
= $3500 + $420 = $3920
Thus, Amount (A) to be paid = $3920 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3500, the simple interest in 1 year
= 6/100 × 3500
= 6 × 3500/100
= 21000/100 = $210
Thus, simple interest for 1 year = $210
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $210 × 2 = $420
Thus, Simple Interest (SI) = $420
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $420
= $3920
Thus, Amount to be paid = $3920 Answer
Similar Questions
(1) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
(2) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(4) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?
(6) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.
(9) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.