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) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(2) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 2% simple interest?
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?
(5) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.
(7) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 4 years.
(9) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(10) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.