Question:
Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
Correct Answer
$4420
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 10%
Time (t) = 3 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% × 3
= $3400 ×10/100 × 3
= 3400 × 10 × 3/100
= 34000 × 3/100
= 102000/100
= $1020
Thus, Simple Interest = $1020
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 + $1020
= $4420
Thus, Amount to be paid = $4420 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) = 3 years
Thus, Amount (A)
= $3400 + ($3400 × 10% × 3)
= $3400 + ($3400 ×10/100 × 3)
= $3400 + (3400 × 10 × 3/100)
= $3400 + (34000 × 3/100)
= $3400 + (102000/100)
= $3400 + $1020 = $4420
Thus, Amount (A) to be paid = $4420 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 3 years
= Simple interest for 1 year × 3
= $340 × 3 = $1020
Thus, Simple Interest (SI) = $1020
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1020
= $4420
Thus, Amount to be paid = $4420 Answer
Similar Questions
(1) Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(3) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(5) If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(7) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 8 years.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.