Question:
Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.
Correct Answer
$5135
Solution And Explanation
Solution
Given,
Principal (P) = $3950
Rate of Simple Interest (SI) = 10%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 3
= $3950 ×10/100 × 3
= 3950 × 10 × 3/100
= 39500 × 3/100
= 118500/100
= $1185
Thus, Simple Interest = $1185
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 + $1185
= $5135
Thus, Amount to be paid = $5135 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) = 10%
And, Time (t) = 3 years
Thus, Amount (A)
= $3950 + ($3950 × 10% × 3)
= $3950 + ($3950 ×10/100 × 3)
= $3950 + (3950 × 10 × 3/100)
= $3950 + (39500 × 3/100)
= $3950 + (118500/100)
= $3950 + $1185 = $5135
Thus, Amount (A) to be paid = $5135 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3950, the simple interest in 1 year
= 10/100 × 3950
= 10 × 3950/100
= 39500/100 = $395
Thus, simple interest for 1 year = $395
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $395 × 3 = $1185
Thus, Simple Interest (SI) = $1185
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3950 + $1185
= $5135
Thus, Amount to be paid = $5135 Answer
Similar Questions
(1) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 7% simple interest?
(2) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?
(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
(5) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.
(6) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.
(8) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.
(9) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?