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) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?
(2) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.
(4) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?
(6) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(7) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(9) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.