Question:
What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?
Correct Answer
$5621
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 9%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 6
= $3650 ×9/100 × 6
= 3650 × 9 × 6/100
= 32850 × 6/100
= 197100/100
= $1971
Thus, Simple Interest = $1971
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 + $1971
= $5621
Thus, Amount to be paid = $5621 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) = 9%
And, Time (t) = 6 years
Thus, Amount (A)
= $3650 + ($3650 × 9% × 6)
= $3650 + ($3650 ×9/100 × 6)
= $3650 + (3650 × 9 × 6/100)
= $3650 + (32850 × 6/100)
= $3650 + (197100/100)
= $3650 + $1971 = $5621
Thus, Amount (A) to be paid = $5621 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3650, the simple interest in 1 year
= 9/100 × 3650
= 9 × 3650/100
= 32850/100 = $328.5
Thus, simple interest for 1 year = $328.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $328.5 × 6 = $1971
Thus, Simple Interest (SI) = $1971
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $1971
= $5621
Thus, Amount to be paid = $5621 Answer
Similar Questions
(1) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.
(3) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(4) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(5) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(6) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?
(7) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?
(9) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.