Question:
Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.
Correct Answer
$8140
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5500 × 6% × 8
= $5500 ×6/100 × 8
= 5500 × 6 × 8/100
= 33000 × 8/100
= 264000/100
= $2640
Thus, Simple Interest = $2640
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 = $5500 + $2640
= $8140
Thus, Amount to be paid = $8140 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 = $5500
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5500 + ($5500 × 6% × 8)
= $5500 + ($5500 ×6/100 × 8)
= $5500 + (5500 × 6 × 8/100)
= $5500 + (33000 × 8/100)
= $5500 + (264000/100)
= $5500 + $2640 = $8140
Thus, Amount (A) to be paid = $8140 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5500, the simple interest in 1 year
= 6/100 × 5500
= 6 × 5500/100
= 33000/100 = $330
Thus, simple interest for 1 year = $330
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $330 × 8 = $2640
Thus, Simple Interest (SI) = $2640
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $2640
= $8140
Thus, Amount to be paid = $8140 Answer
Similar Questions
(1) 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.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.
(3) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(4) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?
(7) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.
(9) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(10) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.