Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
Correct Answer
$8313
Solution And Explanation
Solution
Given,
Principal (P) = $5100
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) = $5100 × 9% × 7
= $5100 ×9/100 × 7
= 5100 × 9 × 7/100
= 45900 × 7/100
= 321300/100
= $3213
Thus, Simple Interest = $3213
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 + $3213
= $8313
Thus, Amount to be paid = $8313 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) = 7 years
Thus, Amount (A)
= $5100 + ($5100 × 9% × 7)
= $5100 + ($5100 ×9/100 × 7)
= $5100 + (5100 × 9 × 7/100)
= $5100 + (45900 × 7/100)
= $5100 + (321300/100)
= $5100 + $3213 = $8313
Thus, Amount (A) to be paid = $8313 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 7 years
= Simple interest for 1 year × 7
= $459 × 7 = $3213
Thus, Simple Interest (SI) = $3213
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $3213
= $8313
Thus, Amount to be paid = $8313 Answer
Similar Questions
(1) How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 7 years.
(3) How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?
(4) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?
(5) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.
(8) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.