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) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(3) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?
(4) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?
(5) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(7) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(8) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.
(10) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.