Question:
Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
Correct Answer
$4114
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 7%
Time (t) = 3 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) = $3400 × 7% × 3
= $3400 ×7/100 × 3
= 3400 × 7 × 3/100
= 23800 × 3/100
= 71400/100
= $714
Thus, Simple Interest = $714
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 + $714
= $4114
Thus, Amount to be paid = $4114 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) = 7%
And, Time (t) = 3 years
Thus, Amount (A)
= $3400 + ($3400 × 7% × 3)
= $3400 + ($3400 ×7/100 × 3)
= $3400 + (3400 × 7 × 3/100)
= $3400 + (23800 × 3/100)
= $3400 + (71400/100)
= $3400 + $714 = $4114
Thus, Amount (A) to be paid = $4114 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 $3400, the simple interest in 1 year
= 7/100 × 3400
= 7 × 3400/100
= 23800/100 = $238
Thus, simple interest for 1 year = $238
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $238 × 3 = $714
Thus, Simple Interest (SI) = $714
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $714
= $4114
Thus, Amount to be paid = $4114 Answer
Similar Questions
(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 4% simple interest?
(2) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(3) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.
(6) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(7) If Jessica borrowed $3750 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.