Question:
What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
Correct Answer
$4880
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 10%
Time (t) = 6 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) = $3050 × 10% × 6
= $3050 ×10/100 × 6
= 3050 × 10 × 6/100
= 30500 × 6/100
= 183000/100
= $1830
Thus, Simple Interest = $1830
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 + $1830
= $4880
Thus, Amount to be paid = $4880 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) = 10%
And, Time (t) = 6 years
Thus, Amount (A)
= $3050 + ($3050 × 10% × 6)
= $3050 + ($3050 ×10/100 × 6)
= $3050 + (3050 × 10 × 6/100)
= $3050 + (30500 × 6/100)
= $3050 + (183000/100)
= $3050 + $1830 = $4880
Thus, Amount (A) to be paid = $4880 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 $3050, the simple interest in 1 year
= 10/100 × 3050
= 10 × 3050/100
= 30500/100 = $305
Thus, simple interest for 1 year = $305
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $305 × 6 = $1830
Thus, Simple Interest (SI) = $1830
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $1830
= $4880
Thus, Amount to be paid = $4880 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?
(2) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?
(3) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?
(4) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.
(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(7) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.
(9) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?
(10) How much loan did Kevin borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8520 to clear it?