Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
Correct Answer
$8231.5
Solution And Explanation
Solution
Given,
Principal (P) = $5050
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) = $5050 × 7% × 9
= $5050 ×7/100 × 9
= 5050 × 7 × 9/100
= 35350 × 9/100
= 318150/100
= $3181.5
Thus, Simple Interest = $3181.5
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 = $5050 + $3181.5
= $8231.5
Thus, Amount to be paid = $8231.5 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 = $5050
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 7% × 9)
= $5050 + ($5050 ×7/100 × 9)
= $5050 + (5050 × 7 × 9/100)
= $5050 + (35350 × 9/100)
= $5050 + (318150/100)
= $5050 + $3181.5 = $8231.5
Thus, Amount (A) to be paid = $8231.5 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 $5050, the simple interest in 1 year
= 7/100 × 5050
= 7 × 5050/100
= 35350/100 = $353.5
Thus, simple interest for 1 year = $353.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $353.5 × 9 = $3181.5
Thus, Simple Interest (SI) = $3181.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $3181.5
= $8231.5
Thus, Amount to be paid = $8231.5 Answer
Similar Questions
(1) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.
(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(5) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(7) If Kimberly paid $5208 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(9) If Karen borrowed $3950 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.