Question:
What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?
Correct Answer
$3780
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 4%
Time (t) = 2 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) = $3500 × 4% × 2
= $3500 ×4/100 × 2
= 3500 × 4 × 2/100
= 14000 × 2/100
= 28000/100
= $280
Thus, Simple Interest = $280
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 + $280
= $3780
Thus, Amount to be paid = $3780 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) = 4%
And, Time (t) = 2 years
Thus, Amount (A)
= $3500 + ($3500 × 4% × 2)
= $3500 + ($3500 ×4/100 × 2)
= $3500 + (3500 × 4 × 2/100)
= $3500 + (14000 × 2/100)
= $3500 + (28000/100)
= $3500 + $280 = $3780
Thus, Amount (A) to be paid = $3780 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 $3500, the simple interest in 1 year
= 4/100 × 3500
= 4 × 3500/100
= 14000/100 = $140
Thus, simple interest for 1 year = $140
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $140 × 2 = $280
Thus, Simple Interest (SI) = $280
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $280
= $3780
Thus, Amount to be paid = $3780 Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(2) Margaret had to pay $4741.5 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 Richard borrowed a sum of $5600 at 4% simple interest for 8 years.
(4) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(5) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(10) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.