Question:
What amount does David have to pay after 5 years if he takes a loan of $3400 at 10% simple interest?
Correct Answer
$5100
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 10%
Time (t) = 5 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) = $3400 × 10% × 5
= $3400 ×10/100 × 5
= 3400 × 10 × 5/100
= 34000 × 5/100
= 170000/100
= $1700
Thus, Simple Interest = $1700
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 = $3400 + $1700
= $5100
Thus, Amount to be paid = $5100 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 = $3400
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3400 + ($3400 × 10% × 5)
= $3400 + ($3400 ×10/100 × 5)
= $3400 + (3400 × 10 × 5/100)
= $3400 + (34000 × 5/100)
= $3400 + (170000/100)
= $3400 + $1700 = $5100
Thus, Amount (A) to be paid = $5100 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 $3400, the simple interest in 1 year
= 10/100 × 3400
= 10 × 3400/100
= 34000/100 = $340
Thus, simple interest for 1 year = $340
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $340 × 5 = $1700
Thus, Simple Interest (SI) = $1700
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1700
= $5100
Thus, Amount to be paid = $5100 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(3) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.
(5) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(6) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?
(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(8) How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.
(10) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?