Question:
What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?
Correct Answer
$5760
Solution And Explanation
Solution
Given,
Principal (P) = $3600
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) = $3600 × 10% × 6
= $3600 ×10/100 × 6
= 3600 × 10 × 6/100
= 36000 × 6/100
= 216000/100
= $2160
Thus, Simple Interest = $2160
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 + $2160
= $5760
Thus, Amount to be paid = $5760 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) = 10%
And, Time (t) = 6 years
Thus, Amount (A)
= $3600 + ($3600 × 10% × 6)
= $3600 + ($3600 ×10/100 × 6)
= $3600 + (3600 × 10 × 6/100)
= $3600 + (36000 × 6/100)
= $3600 + (216000/100)
= $3600 + $2160 = $5760
Thus, Amount (A) to be paid = $5760 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 $3600, the simple interest in 1 year
= 10/100 × 3600
= 10 × 3600/100
= 36000/100 = $360
Thus, simple interest for 1 year = $360
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $360 × 6 = $2160
Thus, Simple Interest (SI) = $2160
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3600 + $2160
= $5760
Thus, Amount to be paid = $5760 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
(4) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.
(5) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?
(7) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?
(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(10) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.