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) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?
(2) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?
(5) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.
(6) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(7) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(8) Thomas had to pay $4370 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.