Question:
Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.
Correct Answer
$4508.5
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 9%
Time (t) = 3 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) = $3550 × 9% × 3
= $3550 ×9/100 × 3
= 3550 × 9 × 3/100
= 31950 × 3/100
= 95850/100
= $958.5
Thus, Simple Interest = $958.5
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 = $3550 + $958.5
= $4508.5
Thus, Amount to be paid = $4508.5 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 = $3550
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 3 years
Thus, Amount (A)
= $3550 + ($3550 × 9% × 3)
= $3550 + ($3550 ×9/100 × 3)
= $3550 + (3550 × 9 × 3/100)
= $3550 + (31950 × 3/100)
= $3550 + (95850/100)
= $3550 + $958.5 = $4508.5
Thus, Amount (A) to be paid = $4508.5 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 $3550, the simple interest in 1 year
= 9/100 × 3550
= 9 × 3550/100
= 31950/100 = $319.5
Thus, simple interest for 1 year = $319.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $319.5 × 3 = $958.5
Thus, Simple Interest (SI) = $958.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $958.5
= $4508.5
Thus, Amount to be paid = $4508.5 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.
(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.
(4) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?
(5) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?
(7) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?
(8) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
(9) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.