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) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(2) If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.
(4) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.
(5) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(8) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(10) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.