Question:
Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.
Correct Answer
$3706
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 3%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 3
= $3400 ×3/100 × 3
= 3400 × 3 × 3/100
= 10200 × 3/100
= 30600/100
= $306
Thus, Simple Interest = $306
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 + $306
= $3706
Thus, Amount to be paid = $3706 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) = 3%
And, Time (t) = 3 years
Thus, Amount (A)
= $3400 + ($3400 × 3% × 3)
= $3400 + ($3400 ×3/100 × 3)
= $3400 + (3400 × 3 × 3/100)
= $3400 + (10200 × 3/100)
= $3400 + (30600/100)
= $3400 + $306 = $3706
Thus, Amount (A) to be paid = $3706 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3400, the simple interest in 1 year
= 3/100 × 3400
= 3 × 3400/100
= 10200/100 = $102
Thus, simple interest for 1 year = $102
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $102 × 3 = $306
Thus, Simple Interest (SI) = $306
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $306
= $3706
Thus, Amount to be paid = $3706 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(2) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(3) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(4) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(5) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?
(6) Kenneth had to pay $5300 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 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.
(9) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.
(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?