Question:
Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.
Correct Answer
$8140
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5500 ×6/100 × 8
= 5500 × 6 × 8/100
= 33000 × 8/100
= 264000/100
= $2640
Thus, Simple Interest = $2640
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 + $2640
= $8140
Thus, Amount to be paid = $8140 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5500 + ($5500 × 6% × 8)
= $5500 + ($5500 ×6/100 × 8)
= $5500 + (5500 × 6 × 8/100)
= $5500 + (33000 × 8/100)
= $5500 + (264000/100)
= $5500 + $2640 = $8140
Thus, Amount (A) to be paid = $8140 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5500, the simple interest in 1 year
= 6/100 × 5500
= 6 × 5500/100
= 33000/100 = $330
Thus, simple interest for 1 year = $330
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $330 × 8 = $2640
Thus, Simple Interest (SI) = $2640
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $2640
= $8140
Thus, Amount to be paid = $8140 Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?
(4) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.
(5) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.
(7) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
(8) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(9) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.