Question:
Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.
Correct Answer
$9460
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 9%
Time (t) = 8 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% × 8
= $5500 ×9/100 × 8
= 5500 × 9 × 8/100
= 49500 × 8/100
= 396000/100
= $3960
Thus, Simple Interest = $3960
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 + $3960
= $9460
Thus, Amount to be paid = $9460 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) = 8 years
Thus, Amount (A)
= $5500 + ($5500 × 9% × 8)
= $5500 + ($5500 ×9/100 × 8)
= $5500 + (5500 × 9 × 8/100)
= $5500 + (49500 × 8/100)
= $5500 + (396000/100)
= $5500 + $3960 = $9460
Thus, Amount (A) to be paid = $9460 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 8 years
= Simple interest for 1 year × 8
= $495 × 8 = $3960
Thus, Simple Interest (SI) = $3960
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $3960
= $9460
Thus, Amount to be paid = $9460 Answer
Similar Questions
(1) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(3) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 3 years.
(4) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(5) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.
(7) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.
(8) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?
(9) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?