Question:
Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.
Correct Answer
$4760
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 10%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 4
= $3400 ×10/100 × 4
= 3400 × 10 × 4/100
= 34000 × 4/100
= 136000/100
= $1360
Thus, Simple Interest = $1360
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 + $1360
= $4760
Thus, Amount to be paid = $4760 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) = 10%
And, Time (t) = 4 years
Thus, Amount (A)
= $3400 + ($3400 × 10% × 4)
= $3400 + ($3400 ×10/100 × 4)
= $3400 + (3400 × 10 × 4/100)
= $3400 + (34000 × 4/100)
= $3400 + (136000/100)
= $3400 + $1360 = $4760
Thus, Amount (A) to be paid = $4760 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3400, the simple interest in 1 year
= 10/100 × 3400
= 10 × 3400/100
= 34000/100 = $340
Thus, simple interest for 1 year = $340
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $340 × 4 = $1360
Thus, Simple Interest (SI) = $1360
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1360
= $4760
Thus, Amount to be paid = $4760 Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
(2) 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.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.
(4) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.
(9) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(10) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.