Question:
Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.
Correct Answer
$5110
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 10%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 4
= $3650 ×10/100 × 4
= 3650 × 10 × 4/100
= 36500 × 4/100
= 146000/100
= $1460
Thus, Simple Interest = $1460
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 + $1460
= $5110
Thus, Amount to be paid = $5110 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) = 10%
And, Time (t) = 4 years
Thus, Amount (A)
= $3650 + ($3650 × 10% × 4)
= $3650 + ($3650 ×10/100 × 4)
= $3650 + (3650 × 10 × 4/100)
= $3650 + (36500 × 4/100)
= $3650 + (146000/100)
= $3650 + $1460 = $5110
Thus, Amount (A) to be paid = $5110 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3650, the simple interest in 1 year
= 10/100 × 3650
= 10 × 3650/100
= 36500/100 = $365
Thus, simple interest for 1 year = $365
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $365 × 4 = $1460
Thus, Simple Interest (SI) = $1460
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $1460
= $5110
Thus, Amount to be paid = $5110 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(3) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(5) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(6) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(8) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.