Question:
Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
Correct Answer
$9900
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5500 ×10/100 × 8
= 5500 × 10 × 8/100
= 55000 × 8/100
= 440000/100
= $4400
Thus, Simple Interest = $4400
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 + $4400
= $9900
Thus, Amount to be paid = $9900 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5500 + ($5500 × 10% × 8)
= $5500 + ($5500 ×10/100 × 8)
= $5500 + (5500 × 10 × 8/100)
= $5500 + (55000 × 8/100)
= $5500 + (440000/100)
= $5500 + $4400 = $9900
Thus, Amount (A) to be paid = $9900 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5500, the simple interest in 1 year
= 10/100 × 5500
= 10 × 5500/100
= 55000/100 = $550
Thus, simple interest for 1 year = $550
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $550 × 8 = $4400
Thus, Simple Interest (SI) = $4400
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $4400
= $9900
Thus, Amount to be paid = $9900 Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 7 years.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.
(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(5) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?
(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 7% simple interest?
(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(9) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(10) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.