Question:
Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.
Correct Answer
$8965
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 9%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 7
= $5500 ×9/100 × 7
= 5500 × 9 × 7/100
= 49500 × 7/100
= 346500/100
= $3465
Thus, Simple Interest = $3465
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 + $3465
= $8965
Thus, Amount to be paid = $8965 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) = 9%
And, Time (t) = 7 years
Thus, Amount (A)
= $5500 + ($5500 × 9% × 7)
= $5500 + ($5500 ×9/100 × 7)
= $5500 + (5500 × 9 × 7/100)
= $5500 + (49500 × 7/100)
= $5500 + (346500/100)
= $5500 + $3465 = $8965
Thus, Amount (A) to be paid = $8965 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5500, the simple interest in 1 year
= 9/100 × 5500
= 9 × 5500/100
= 49500/100 = $495
Thus, simple interest for 1 year = $495
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $495 × 7 = $3465
Thus, Simple Interest (SI) = $3465
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $3465
= $8965
Thus, Amount to be paid = $8965 Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(2) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(3) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(4) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(6) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 3 years.
(8) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 4 years.
(10) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.