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) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.
(2) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6812.5 to clear it?
(3) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(4) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(6) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?
(9) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(10) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.