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) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(2) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?
(4) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 4 years.
(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(7) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(9) If Donna paid $5238 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?