Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
Correct Answer
$9231
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 9%
Time (t) = 9 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) = $5100 × 9% × 9
= $5100 ×9/100 × 9
= 5100 × 9 × 9/100
= 45900 × 9/100
= 413100/100
= $4131
Thus, Simple Interest = $4131
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 = $5100 + $4131
= $9231
Thus, Amount to be paid = $9231 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 = $5100
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 9% × 9)
= $5100 + ($5100 ×9/100 × 9)
= $5100 + (5100 × 9 × 9/100)
= $5100 + (45900 × 9/100)
= $5100 + (413100/100)
= $5100 + $4131 = $9231
Thus, Amount (A) to be paid = $9231 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 $5100, the simple interest in 1 year
= 9/100 × 5100
= 9 × 5100/100
= 45900/100 = $459
Thus, simple interest for 1 year = $459
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $459 × 9 = $4131
Thus, Simple Interest (SI) = $4131
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $4131
= $9231
Thus, Amount to be paid = $9231 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?
(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?
(5) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?
(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(8) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?
(9) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?
(10) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.