Question:
Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
Correct Answer
$7700
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5500 ×5/100 × 8
= 5500 × 5 × 8/100
= 27500 × 8/100
= 220000/100
= $2200
Thus, Simple Interest = $2200
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 + $2200
= $7700
Thus, Amount to be paid = $7700 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5500 + ($5500 × 5% × 8)
= $5500 + ($5500 ×5/100 × 8)
= $5500 + (5500 × 5 × 8/100)
= $5500 + (27500 × 8/100)
= $5500 + (220000/100)
= $5500 + $2200 = $7700
Thus, Amount (A) to be paid = $7700 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5500, the simple interest in 1 year
= 5/100 × 5500
= 5 × 5500/100
= 27500/100 = $275
Thus, simple interest for 1 year = $275
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $275 × 8 = $2200
Thus, Simple Interest (SI) = $2200
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $2200
= $7700
Thus, Amount to be paid = $7700 Answer
Similar Questions
(1) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.
(3) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(5) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.
(7) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(9) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?