Question:
Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.
Correct Answer
$8580
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5500 ×7/100 × 8
= 5500 × 7 × 8/100
= 38500 × 8/100
= 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5500 + ($5500 × 7% × 8)
= $5500 + ($5500 ×7/100 × 8)
= $5500 + (5500 × 7 × 8/100)
= $5500 + (38500 × 8/100)
= $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 = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5500, the simple interest in 1 year
= 7/100 × 5500
= 7 × 5500/100
= 38500/100 = $385
Thus, simple interest for 1 year = $385
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $385 × 8 = $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) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(3) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
(4) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(6) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(7) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.