Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.
Correct Answer
$8032.5
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 7
= $5950 ×5/100 × 7
= 5950 × 5 × 7/100
= 29750 × 7/100
= 208250/100
= $2082.5
Thus, Simple Interest = $2082.5
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 + $2082.5
= $8032.5
Thus, Amount to be paid = $8032.5 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) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5950 + ($5950 × 5% × 7)
= $5950 + ($5950 ×5/100 × 7)
= $5950 + (5950 × 5 × 7/100)
= $5950 + (29750 × 7/100)
= $5950 + (208250/100)
= $5950 + $2082.5 = $8032.5
Thus, Amount (A) to be paid = $8032.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5950, the simple interest in 1 year
= 5/100 × 5950
= 5 × 5950/100
= 29750/100 = $297.5
Thus, simple interest for 1 year = $297.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $297.5 × 7 = $2082.5
Thus, Simple Interest (SI) = $2082.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $2082.5
= $8032.5
Thus, Amount to be paid = $8032.5 Answer
Similar Questions
(1) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
(2) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(3) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(5) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
(6) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 8 years.
(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.
(9) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.