Question:
Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.
Correct Answer
$6380
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 2%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 8
= $5500 ×2/100 × 8
= 5500 × 2 × 8/100
= 11000 × 8/100
= 88000/100
= $880
Thus, Simple Interest = $880
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 + $880
= $6380
Thus, Amount to be paid = $6380 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) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5500 + ($5500 × 2% × 8)
= $5500 + ($5500 ×2/100 × 8)
= $5500 + (5500 × 2 × 8/100)
= $5500 + (11000 × 8/100)
= $5500 + (88000/100)
= $5500 + $880 = $6380
Thus, Amount (A) to be paid = $6380 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5500, the simple interest in 1 year
= 2/100 × 5500
= 2 × 5500/100
= 11000/100 = $110
Thus, simple interest for 1 year = $110
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $110 × 8 = $880
Thus, Simple Interest (SI) = $880
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $880
= $6380
Thus, Amount to be paid = $6380 Answer
Similar Questions
(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?
(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.
(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?
(5) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?
(7) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
(9) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.