Question:
Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.
Correct Answer
$3808
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 4%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 3
= $3400 ×4/100 × 3
= 3400 × 4 × 3/100
= 13600 × 3/100
= 40800/100
= $408
Thus, Simple Interest = $408
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 + $408
= $3808
Thus, Amount to be paid = $3808 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) = 4%
And, Time (t) = 3 years
Thus, Amount (A)
= $3400 + ($3400 × 4% × 3)
= $3400 + ($3400 ×4/100 × 3)
= $3400 + (3400 × 4 × 3/100)
= $3400 + (13600 × 3/100)
= $3400 + (40800/100)
= $3400 + $408 = $3808
Thus, Amount (A) to be paid = $3808 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3400, the simple interest in 1 year
= 4/100 × 3400
= 4 × 3400/100
= 13600/100 = $136
Thus, simple interest for 1 year = $136
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $136 × 3 = $408
Thus, Simple Interest (SI) = $408
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $408
= $3808
Thus, Amount to be paid = $3808 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 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 3% simple interest for 3 years.
(3) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?
(5) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(6) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(8) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
(10) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.