Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
Correct Answer
$8800
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 6%
Time (t) = 10 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% × 10
= $5500 ×6/100 × 10
= 5500 × 6 × 10/100
= 33000 × 10/100
= 330000/100
= $3300
Thus, Simple Interest = $3300
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 + $3300
= $8800
Thus, Amount to be paid = $8800 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) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 6% × 10)
= $5500 + ($5500 ×6/100 × 10)
= $5500 + (5500 × 6 × 10/100)
= $5500 + (33000 × 10/100)
= $5500 + (330000/100)
= $5500 + $3300 = $8800
Thus, Amount (A) to be paid = $8800 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 10 years
= Simple interest for 1 year × 10
= $330 × 10 = $3300
Thus, Simple Interest (SI) = $3300
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $3300
= $8800
Thus, Amount to be paid = $8800 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.
(4) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 4 years.
(9) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(10) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.