Question:
Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.
Correct Answer
$4542.5
Solution And Explanation
Solution
Given,
Principal (P) = $3950
Rate of Simple Interest (SI) = 5%
Time (t) = 3 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% × 3
= $3950 ×5/100 × 3
= 3950 × 5 × 3/100
= 19750 × 3/100
= 59250/100
= $592.5
Thus, Simple Interest = $592.5
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 + $592.5
= $4542.5
Thus, Amount to be paid = $4542.5 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) = 3 years
Thus, Amount (A)
= $3950 + ($3950 × 5% × 3)
= $3950 + ($3950 ×5/100 × 3)
= $3950 + (3950 × 5 × 3/100)
= $3950 + (19750 × 3/100)
= $3950 + (59250/100)
= $3950 + $592.5 = $4542.5
Thus, Amount (A) to be paid = $4542.5 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 3 years
= Simple interest for 1 year × 3
= $197.5 × 3 = $592.5
Thus, Simple Interest (SI) = $592.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3950 + $592.5
= $4542.5
Thus, Amount to be paid = $4542.5 Answer
Similar Questions
(1) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.
(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(3) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?
(5) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.
(7) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.
(9) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(10) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?