Question:
Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.
Correct Answer
$4082.5
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 5%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 3
= $3550 ×5/100 × 3
= 3550 × 5 × 3/100
= 17750 × 3/100
= 53250/100
= $532.5
Thus, Simple Interest = $532.5
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 + $532.5
= $4082.5
Thus, Amount to be paid = $4082.5 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) = 5%
And, Time (t) = 3 years
Thus, Amount (A)
= $3550 + ($3550 × 5% × 3)
= $3550 + ($3550 ×5/100 × 3)
= $3550 + (3550 × 5 × 3/100)
= $3550 + (17750 × 3/100)
= $3550 + (53250/100)
= $3550 + $532.5 = $4082.5
Thus, Amount (A) to be paid = $4082.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3550, the simple interest in 1 year
= 5/100 × 3550
= 5 × 3550/100
= 17750/100 = $177.5
Thus, simple interest for 1 year = $177.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $177.5 × 3 = $532.5
Thus, Simple Interest (SI) = $532.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $532.5
= $4082.5
Thus, Amount to be paid = $4082.5 Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(3) If Karen borrowed $3950 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?
(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?
(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(8) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
(9) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.