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) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?
(3) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(5) 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.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 4 years.
(7) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(8) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(9) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?
(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 2% simple interest?