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) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(2) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.
(4) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(5) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
(6) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(7) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?
(9) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(10) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.