Question:
Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.
Correct Answer
$4307
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 6%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $3650 × 6% × 3
= $3650 ×6/100 × 3
= 3650 × 6 × 3/100
= 21900 × 3/100
= 65700/100
= $657
Thus, Simple Interest = $657
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 = $3650 + $657
= $4307
Thus, Amount to be paid = $4307 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 = $3650
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 3 years
Thus, Amount (A)
= $3650 + ($3650 × 6% × 3)
= $3650 + ($3650 ×6/100 × 3)
= $3650 + (3650 × 6 × 3/100)
= $3650 + (21900 × 3/100)
= $3650 + (65700/100)
= $3650 + $657 = $4307
Thus, Amount (A) to be paid = $4307 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3650, the simple interest in 1 year
= 6/100 × 3650
= 6 × 3650/100
= 21900/100 = $219
Thus, simple interest for 1 year = $219
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $219 × 3 = $657
Thus, Simple Interest (SI) = $657
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $657
= $4307
Thus, Amount to be paid = $4307 Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(2) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?
(3) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(5) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?
(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(9) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
(10) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.