Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.
Correct Answer
$7378
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5950 ×3/100 × 8
= 5950 × 3 × 8/100
= 17850 × 8/100
= 142800/100
= $1428
Thus, Simple Interest = $1428
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 + $1428
= $7378
Thus, Amount to be paid = $7378 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5950 + ($5950 × 3% × 8)
= $5950 + ($5950 ×3/100 × 8)
= $5950 + (5950 × 3 × 8/100)
= $5950 + (17850 × 8/100)
= $5950 + (142800/100)
= $5950 + $1428 = $7378
Thus, Amount (A) to be paid = $7378 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5950, the simple interest in 1 year
= 3/100 × 5950
= 3 × 5950/100
= 17850/100 = $178.5
Thus, simple interest for 1 year = $178.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $178.5 × 8 = $1428
Thus, Simple Interest (SI) = $1428
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $1428
= $7378
Thus, Amount to be paid = $7378 Answer
Similar Questions
(1) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?
(2) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(4) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(7) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.
(9) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.