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) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?
(3) 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.
(4) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(6) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(9) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?