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) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(3) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.
(6) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?
(7) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(8) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(9) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?