Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
Correct Answer
$10769.5
Solution And Explanation
Solution
Given,
Principal (P) = $5950
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) = $5950 × 9% × 9
= $5950 ×9/100 × 9
= 5950 × 9 × 9/100
= 53550 × 9/100
= 481950/100
= $4819.5
Thus, Simple Interest = $4819.5
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 + $4819.5
= $10769.5
Thus, Amount to be paid = $10769.5 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) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 9% × 9)
= $5950 + ($5950 ×9/100 × 9)
= $5950 + (5950 × 9 × 9/100)
= $5950 + (53550 × 9/100)
= $5950 + (481950/100)
= $5950 + $4819.5 = $10769.5
Thus, Amount (A) to be paid = $10769.5 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 9 years
= Simple interest for 1 year × 9
= $535.5 × 9 = $4819.5
Thus, Simple Interest (SI) = $4819.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $4819.5
= $10769.5
Thus, Amount to be paid = $10769.5 Answer
Similar Questions
(1) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?
(2) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.
(4) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 4 years.
(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(7) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(8) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?
(10) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.