Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.
Correct Answer
$8231.5
Solution And Explanation
Solution
Given,
Principal (P) = $5050
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) = $5050 × 9% × 7
= $5050 ×9/100 × 7
= 5050 × 9 × 7/100
= 45450 × 7/100
= 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) = 9%
And, Time (t) = 7 years
Thus, Amount (A)
= $5050 + ($5050 × 9% × 7)
= $5050 + ($5050 ×9/100 × 7)
= $5050 + (5050 × 9 × 7/100)
= $5050 + (45450 × 7/100)
= $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 = 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 $5050, the simple interest in 1 year
= 9/100 × 5050
= 9 × 5050/100
= 45450/100 = $454.5
Thus, simple interest for 1 year = $454.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $454.5 × 7 = $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) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(3) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?
(5) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.
(8) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if James borrowed a sum of $3000 at a 9% simple interest?
(10) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.