Question:
What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 5% simple interest?
Correct Answer
$4680
Solution And Explanation
Solution
Given,
Principal (P) = $3600
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) = $3600 × 5% × 6
= $3600 ×5/100 × 6
= 3600 × 5 × 6/100
= 18000 × 6/100
= 108000/100
= $1080
Thus, Simple Interest = $1080
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 = $3600 + $1080
= $4680
Thus, Amount to be paid = $4680 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 = $3600
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3600 + ($3600 × 5% × 6)
= $3600 + ($3600 ×5/100 × 6)
= $3600 + (3600 × 5 × 6/100)
= $3600 + (18000 × 6/100)
= $3600 + (108000/100)
= $3600 + $1080 = $4680
Thus, Amount (A) to be paid = $4680 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 $3600, the simple interest in 1 year
= 5/100 × 3600
= 5 × 3600/100
= 18000/100 = $180
Thus, simple interest for 1 year = $180
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $180 × 6 = $1080
Thus, Simple Interest (SI) = $1080
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3600 + $1080
= $4680
Thus, Amount to be paid = $4680 Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 8 years.
(3) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?
(4) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?
(5) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(8) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?
(9) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?
(10) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.