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) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?
(2) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.
(5) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(6) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?
(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?
(9) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?