Question:
Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
Correct Answer
$8965
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 7%
Time (t) = 9 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% × 9
= $5500 ×7/100 × 9
= 5500 × 7 × 9/100
= 38500 × 9/100
= 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) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5500 + ($5500 × 7% × 9)
= $5500 + ($5500 ×7/100 × 9)
= $5500 + (5500 × 7 × 9/100)
= $5500 + (38500 × 9/100)
= $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 = 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 9 years
= Simple interest for 1 year × 9
= $385 × 9 = $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) 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.
(2) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 3 years.
(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(4) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.
(5) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.
(8) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.