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) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.
(3) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?
(4) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
(5) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(6) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(7) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(8) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?
(9) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(10) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?