Question:
Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
Correct Answer
$8470
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 9
= $5500 ×6/100 × 9
= 5500 × 6 × 9/100
= 33000 × 9/100
= 297000/100
= $2970
Thus, Simple Interest = $2970
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 + $2970
= $8470
Thus, Amount to be paid = $8470 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5500 + ($5500 × 6% × 9)
= $5500 + ($5500 ×6/100 × 9)
= $5500 + (5500 × 6 × 9/100)
= $5500 + (33000 × 9/100)
= $5500 + (297000/100)
= $5500 + $2970 = $8470
Thus, Amount (A) to be paid = $8470 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5500, the simple interest in 1 year
= 6/100 × 5500
= 6 × 5500/100
= 33000/100 = $330
Thus, simple interest for 1 year = $330
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $330 × 9 = $2970
Thus, Simple Interest (SI) = $2970
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $2970
= $8470
Thus, Amount to be paid = $8470 Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?
(2) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(3) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 4% simple interest?
(4) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(6) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?
(8) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.