Question:
What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?
Correct Answer
$5550
Solution And Explanation
Solution
Given,
Principal (P) = $3700
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) = $3700 × 10% × 5
= $3700 ×10/100 × 5
= 3700 × 10 × 5/100
= 37000 × 5/100
= 185000/100
= $1850
Thus, Simple Interest = $1850
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 = $3700 + $1850
= $5550
Thus, Amount to be paid = $5550 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 = $3700
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3700 + ($3700 × 10% × 5)
= $3700 + ($3700 ×10/100 × 5)
= $3700 + (3700 × 10 × 5/100)
= $3700 + (37000 × 5/100)
= $3700 + (185000/100)
= $3700 + $1850 = $5550
Thus, Amount (A) to be paid = $5550 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 $3700, the simple interest in 1 year
= 10/100 × 3700
= 10 × 3700/100
= 37000/100 = $370
Thus, simple interest for 1 year = $370
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $370 × 5 = $1850
Thus, Simple Interest (SI) = $1850
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3700 + $1850
= $5550
Thus, Amount to be paid = $5550 Answer
Similar Questions
(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.
(2) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.
(4) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(6) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.
(8) How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?
(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.
(10) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.