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) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
(2) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.
(4) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?
(5) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(6) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.
(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(10) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.