Question:
Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.
Correct Answer
$4745
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 10%
Time (t) = 3 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% × 3
= $3650 ×10/100 × 3
= 3650 × 10 × 3/100
= 36500 × 3/100
= 109500/100
= $1095
Thus, Simple Interest = $1095
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 + $1095
= $4745
Thus, Amount to be paid = $4745 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) = 3 years
Thus, Amount (A)
= $3650 + ($3650 × 10% × 3)
= $3650 + ($3650 ×10/100 × 3)
= $3650 + (3650 × 10 × 3/100)
= $3650 + (36500 × 3/100)
= $3650 + (109500/100)
= $3650 + $1095 = $4745
Thus, Amount (A) to be paid = $4745 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 3 years
= Simple interest for 1 year × 3
= $365 × 3 = $1095
Thus, Simple Interest (SI) = $1095
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $1095
= $4745
Thus, Amount to be paid = $4745 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(2) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.
(4) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.
(5) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?
(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.