Question:
Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.
Correct Answer
$4402
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 8%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 3
= $3550 ×8/100 × 3
= 3550 × 8 × 3/100
= 28400 × 3/100
= 85200/100
= $852
Thus, Simple Interest = $852
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 + $852
= $4402
Thus, Amount to be paid = $4402 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) = 8%
And, Time (t) = 3 years
Thus, Amount (A)
= $3550 + ($3550 × 8% × 3)
= $3550 + ($3550 ×8/100 × 3)
= $3550 + (3550 × 8 × 3/100)
= $3550 + (28400 × 3/100)
= $3550 + (85200/100)
= $3550 + $852 = $4402
Thus, Amount (A) to be paid = $4402 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3550, the simple interest in 1 year
= 8/100 × 3550
= 8 × 3550/100
= 28400/100 = $284
Thus, simple interest for 1 year = $284
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $284 × 3 = $852
Thus, Simple Interest (SI) = $852
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $852
= $4402
Thus, Amount to be paid = $4402 Answer
Similar Questions
(1) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?
(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.
(3) If Richard borrowed $3600 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 Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
(5) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.
(6) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.
(7) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(9) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.