Question:
Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.
Correct Answer
$3599
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 6%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $3050 × 6% × 3
= $3050 ×6/100 × 3
= 3050 × 6 × 3/100
= 18300 × 3/100
= 54900/100
= $549
Thus, Simple Interest = $549
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 = $3050 + $549
= $3599
Thus, Amount to be paid = $3599 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 = $3050
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 3 years
Thus, Amount (A)
= $3050 + ($3050 × 6% × 3)
= $3050 + ($3050 ×6/100 × 3)
= $3050 + (3050 × 6 × 3/100)
= $3050 + (18300 × 3/100)
= $3050 + (54900/100)
= $3050 + $549 = $3599
Thus, Amount (A) to be paid = $3599 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3050, the simple interest in 1 year
= 6/100 × 3050
= 6 × 3050/100
= 18300/100 = $183
Thus, simple interest for 1 year = $183
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $183 × 3 = $549
Thus, Simple Interest (SI) = $549
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $549
= $3599
Thus, Amount to be paid = $3599 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?
(2) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(3) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?
(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(6) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(7) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?
(9) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 4 years.