Question:
Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
Correct Answer
$4582
Solution And Explanation
Solution
Given,
Principal (P) = $3950
Rate of Simple Interest (SI) = 4%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $3950 × 4% × 4
= $3950 ×4/100 × 4
= 3950 × 4 × 4/100
= 15800 × 4/100
= 63200/100
= $632
Thus, Simple Interest = $632
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 = $3950 + $632
= $4582
Thus, Amount to be paid = $4582 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 = $3950
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 4 years
Thus, Amount (A)
= $3950 + ($3950 × 4% × 4)
= $3950 + ($3950 ×4/100 × 4)
= $3950 + (3950 × 4 × 4/100)
= $3950 + (15800 × 4/100)
= $3950 + (63200/100)
= $3950 + $632 = $4582
Thus, Amount (A) to be paid = $4582 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3950, the simple interest in 1 year
= 4/100 × 3950
= 4 × 3950/100
= 15800/100 = $158
Thus, simple interest for 1 year = $158
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $158 × 4 = $632
Thus, Simple Interest (SI) = $632
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3950 + $632
= $4582
Thus, Amount to be paid = $4582 Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(2) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) 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?
(5) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(8) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?
(9) Nancy had to pay $4772.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?