Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.
Correct Answer
$9698.5
Solution And Explanation
Solution
Given,
Principal (P) = $5950
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) = $5950 × 9% × 7
= $5950 ×9/100 × 7
= 5950 × 9 × 7/100
= 53550 × 7/100
= 374850/100
= $3748.5
Thus, Simple Interest = $3748.5
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 = $5950 + $3748.5
= $9698.5
Thus, Amount to be paid = $9698.5 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 = $5950
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 7 years
Thus, Amount (A)
= $5950 + ($5950 × 9% × 7)
= $5950 + ($5950 ×9/100 × 7)
= $5950 + (5950 × 9 × 7/100)
= $5950 + (53550 × 7/100)
= $5950 + (374850/100)
= $5950 + $3748.5 = $9698.5
Thus, Amount (A) to be paid = $9698.5 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 $5950, the simple interest in 1 year
= 9/100 × 5950
= 9 × 5950/100
= 53550/100 = $535.5
Thus, simple interest for 1 year = $535.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $535.5 × 7 = $3748.5
Thus, Simple Interest (SI) = $3748.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $3748.5
= $9698.5
Thus, Amount to be paid = $9698.5 Answer
Similar Questions
(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(2) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?
(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(4) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.
(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?
(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(8) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
(10) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.