Question:
Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.
Correct Answer
$8580
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 8%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 7
= $5500 ×8/100 × 7
= 5500 × 8 × 7/100
= 44000 × 7/100
= 308000/100
= $3080
Thus, Simple Interest = $3080
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 + $3080
= $8580
Thus, Amount to be paid = $8580 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) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5500 + ($5500 × 8% × 7)
= $5500 + ($5500 ×8/100 × 7)
= $5500 + (5500 × 8 × 7/100)
= $5500 + (44000 × 7/100)
= $5500 + (308000/100)
= $5500 + $3080 = $8580
Thus, Amount (A) to be paid = $8580 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5500, the simple interest in 1 year
= 8/100 × 5500
= 8 × 5500/100
= 44000/100 = $440
Thus, simple interest for 1 year = $440
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $440 × 7 = $3080
Thus, Simple Interest (SI) = $3080
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $3080
= $8580
Thus, Amount to be paid = $8580 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(2) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(3) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(4) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(6) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.
(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?
(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(10) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?