Question:
What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?
Correct Answer
$3990
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 7%
Time (t) = 2 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) = $3500 × 7% × 2
= $3500 ×7/100 × 2
= 3500 × 7 × 2/100
= 24500 × 2/100
= 49000/100
= $490
Thus, Simple Interest = $490
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 + $490
= $3990
Thus, Amount to be paid = $3990 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) = 7%
And, Time (t) = 2 years
Thus, Amount (A)
= $3500 + ($3500 × 7% × 2)
= $3500 + ($3500 ×7/100 × 2)
= $3500 + (3500 × 7 × 2/100)
= $3500 + (24500 × 2/100)
= $3500 + (49000/100)
= $3500 + $490 = $3990
Thus, Amount (A) to be paid = $3990 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 $3500, the simple interest in 1 year
= 7/100 × 3500
= 7 × 3500/100
= 24500/100 = $245
Thus, simple interest for 1 year = $245
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $245 × 2 = $490
Thus, Simple Interest (SI) = $490
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $490
= $3990
Thus, Amount to be paid = $3990 Answer
Similar Questions
(1) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(2) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.
(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(5) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?
(6) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(7) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(8) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?
(10) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.