Question:
Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.
Correct Answer
$3808
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 3%
Time (t) = 4 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% × 4
= $3400 ×3/100 × 4
= 3400 × 3 × 4/100
= 10200 × 4/100
= 40800/100
= $408
Thus, Simple Interest = $408
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 + $408
= $3808
Thus, Amount to be paid = $3808 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) = 4 years
Thus, Amount (A)
= $3400 + ($3400 × 3% × 4)
= $3400 + ($3400 ×3/100 × 4)
= $3400 + (3400 × 3 × 4/100)
= $3400 + (10200 × 4/100)
= $3400 + (40800/100)
= $3400 + $408 = $3808
Thus, Amount (A) to be paid = $3808 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 4 years
= Simple interest for 1 year × 4
= $102 × 4 = $408
Thus, Simple Interest (SI) = $408
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $408
= $3808
Thus, Amount to be paid = $3808 Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(2) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.
(3) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(4) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(6) How much loan did Kevin borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8520 to clear it?
(7) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.
(8) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.
(10) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?