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) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.
(2) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?
(3) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?
(4) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?
(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(6) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 7 years.
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?
(8) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 4 years.