Question:
What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
Correct Answer
$4562.5
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 5%
Time (t) = 5 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) = $3650 × 5% × 5
= $3650 ×5/100 × 5
= 3650 × 5 × 5/100
= 18250 × 5/100
= 91250/100
= $912.5
Thus, Simple Interest = $912.5
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 = $3650 + $912.5
= $4562.5
Thus, Amount to be paid = $4562.5 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 = $3650
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 5 years
Thus, Amount (A)
= $3650 + ($3650 × 5% × 5)
= $3650 + ($3650 ×5/100 × 5)
= $3650 + (3650 × 5 × 5/100)
= $3650 + (18250 × 5/100)
= $3650 + (91250/100)
= $3650 + $912.5 = $4562.5
Thus, Amount (A) to be paid = $4562.5 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 $3650, the simple interest in 1 year
= 5/100 × 3650
= 5 × 3650/100
= 18250/100 = $182.5
Thus, simple interest for 1 year = $182.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $182.5 × 5 = $912.5
Thus, Simple Interest (SI) = $912.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $912.5
= $4562.5
Thus, Amount to be paid = $4562.5 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
(3) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(4) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?
(6) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?
(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.