Question:
What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?
Correct Answer
$5135
Solution And Explanation
Solution
Given,
Principal (P) = $3950
Rate of Simple Interest (SI) = 5%
Time (t) = 6 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% × 6
= $3950 ×5/100 × 6
= 3950 × 5 × 6/100
= 19750 × 6/100
= 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) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3950 + ($3950 × 5% × 6)
= $3950 + ($3950 ×5/100 × 6)
= $3950 + (3950 × 5 × 6/100)
= $3950 + (19750 × 6/100)
= $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 = 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 6 years
= Simple interest for 1 year × 6
= $197.5 × 6 = $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) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.
(3) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(8) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(9) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(10) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.