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) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
(3) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?
(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(6) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?
(8) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?
(9) How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?
(10) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.