Question:
Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.
Correct Answer
$4624
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 9%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 4
= $3400 ×9/100 × 4
= 3400 × 9 × 4/100
= 30600 × 4/100
= 122400/100
= $1224
Thus, Simple Interest = $1224
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 + $1224
= $4624
Thus, Amount to be paid = $4624 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) = 9%
And, Time (t) = 4 years
Thus, Amount (A)
= $3400 + ($3400 × 9% × 4)
= $3400 + ($3400 ×9/100 × 4)
= $3400 + (3400 × 9 × 4/100)
= $3400 + (30600 × 4/100)
= $3400 + (122400/100)
= $3400 + $1224 = $4624
Thus, Amount (A) to be paid = $4624 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3400, the simple interest in 1 year
= 9/100 × 3400
= 9 × 3400/100
= 30600/100 = $306
Thus, simple interest for 1 year = $306
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $306 × 4 = $1224
Thus, Simple Interest (SI) = $1224
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1224
= $4624
Thus, Amount to be paid = $4624 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.
(3) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(4) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 3 years.
(7) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.
(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 4 years.
(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?