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) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 5% simple interest?
(3) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(5) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?
(6) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(7) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.
(10) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.