Question:
Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.
Correct Answer
$4080
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 5%
Time (t) = 4 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% × 4
= $3400 ×5/100 × 4
= 3400 × 5 × 4/100
= 17000 × 4/100
= 68000/100
= $680
Thus, Simple Interest = $680
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 + $680
= $4080
Thus, Amount to be paid = $4080 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) = 4 years
Thus, Amount (A)
= $3400 + ($3400 × 5% × 4)
= $3400 + ($3400 ×5/100 × 4)
= $3400 + (3400 × 5 × 4/100)
= $3400 + (17000 × 4/100)
= $3400 + (68000/100)
= $3400 + $680 = $4080
Thus, Amount (A) to be paid = $4080 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 4 years
= Simple interest for 1 year × 4
= $170 × 4 = $680
Thus, Simple Interest (SI) = $680
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $680
= $4080
Thus, Amount to be paid = $4080 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.
(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.
(5) How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?
(6) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(7) 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.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(9) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(10) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.