Question:
Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 3 years.
Correct Answer
$3910
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 5%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 3
= $3400 ×5/100 × 3
= 3400 × 5 × 3/100
= 17000 × 3/100
= 51000/100
= $510
Thus, Simple Interest = $510
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 + $510
= $3910
Thus, Amount to be paid = $3910 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) = 5%
And, Time (t) = 3 years
Thus, Amount (A)
= $3400 + ($3400 × 5% × 3)
= $3400 + ($3400 ×5/100 × 3)
= $3400 + (3400 × 5 × 3/100)
= $3400 + (17000 × 3/100)
= $3400 + (51000/100)
= $3400 + $510 = $3910
Thus, Amount (A) to be paid = $3910 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3400, the simple interest in 1 year
= 5/100 × 3400
= 5 × 3400/100
= 17000/100 = $170
Thus, simple interest for 1 year = $170
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $170 × 3 = $510
Thus, Simple Interest (SI) = $510
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $510
= $3910
Thus, Amount to be paid = $3910 Answer
Similar Questions
(1) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
(2) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
(4) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(5) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?
(7) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.