Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.
Correct Answer
$8658
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 8%
Time (t) = 7 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) = $5550 × 8% × 7
= $5550 ×8/100 × 7
= 5550 × 8 × 7/100
= 44400 × 7/100
= 310800/100
= $3108
Thus, Simple Interest = $3108
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 = $5550 + $3108
= $8658
Thus, Amount to be paid = $8658 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 = $5550
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5550 + ($5550 × 8% × 7)
= $5550 + ($5550 ×8/100 × 7)
= $5550 + (5550 × 8 × 7/100)
= $5550 + (44400 × 7/100)
= $5550 + (310800/100)
= $5550 + $3108 = $8658
Thus, Amount (A) to be paid = $8658 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 $5550, the simple interest in 1 year
= 8/100 × 5550
= 8 × 5550/100
= 44400/100 = $444
Thus, simple interest for 1 year = $444
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $444 × 7 = $3108
Thus, Simple Interest (SI) = $3108
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $3108
= $8658
Thus, Amount to be paid = $8658 Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?
(2) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(3) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.
(6) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(10) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.