Question:
What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
Correct Answer
$4937.5
Solution And Explanation
Solution
Given,
Principal (P) = $3950
Rate of Simple Interest (SI) = 5%
Time (t) = 5 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) = $3950 × 5% × 5
= $3950 ×5/100 × 5
= 3950 × 5 × 5/100
= 19750 × 5/100
= 98750/100
= $987.5
Thus, Simple Interest = $987.5
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 = $3950 + $987.5
= $4937.5
Thus, Amount to be paid = $4937.5 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 = $3950
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 5 years
Thus, Amount (A)
= $3950 + ($3950 × 5% × 5)
= $3950 + ($3950 ×5/100 × 5)
= $3950 + (3950 × 5 × 5/100)
= $3950 + (19750 × 5/100)
= $3950 + (98750/100)
= $3950 + $987.5 = $4937.5
Thus, Amount (A) to be paid = $4937.5 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 $3950, the simple interest in 1 year
= 5/100 × 3950
= 5 × 3950/100
= 19750/100 = $197.5
Thus, simple interest for 1 year = $197.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $197.5 × 5 = $987.5
Thus, Simple Interest (SI) = $987.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3950 + $987.5
= $4937.5
Thus, Amount to be paid = $4937.5 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 10% simple interest?
(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 3 years.
(6) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.
(8) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.
(10) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.