Question:
What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
Correct Answer
$4828
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 7%
Time (t) = 6 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% × 6
= $3400 ×7/100 × 6
= 3400 × 7 × 6/100
= 23800 × 6/100
= 142800/100
= $1428
Thus, Simple Interest = $1428
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 + $1428
= $4828
Thus, Amount to be paid = $4828 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) = 6 years
Thus, Amount (A)
= $3400 + ($3400 × 7% × 6)
= $3400 + ($3400 ×7/100 × 6)
= $3400 + (3400 × 7 × 6/100)
= $3400 + (23800 × 6/100)
= $3400 + (142800/100)
= $3400 + $1428 = $4828
Thus, Amount (A) to be paid = $4828 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 6 years
= Simple interest for 1 year × 6
= $238 × 6 = $1428
Thus, Simple Interest (SI) = $1428
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1428
= $4828
Thus, Amount to be paid = $4828 Answer
Similar Questions
(1) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(3) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?
(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.
(6) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.
(10) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?