Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
Correct Answer
$9698.5
Solution And Explanation
Solution
Given,
Principal (P) = $5950
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) = $5950 × 7% × 9
= $5950 ×7/100 × 9
= 5950 × 7 × 9/100
= 41650 × 9/100
= 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) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 7% × 9)
= $5950 + ($5950 ×7/100 × 9)
= $5950 + (5950 × 7 × 9/100)
= $5950 + (41650 × 9/100)
= $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 = 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 $5950, the simple interest in 1 year
= 7/100 × 5950
= 7 × 5950/100
= 41650/100 = $416.5
Thus, simple interest for 1 year = $416.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $416.5 × 9 = $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) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
(3) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?
(4) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 3 years.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.
(7) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(8) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(10) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?