Question:
What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
Correct Answer
$4197.5
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 3%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 5
= $3650 ×3/100 × 5
= 3650 × 3 × 5/100
= 10950 × 5/100
= 54750/100
= $547.5
Thus, Simple Interest = $547.5
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 + $547.5
= $4197.5
Thus, Amount to be paid = $4197.5 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) = 3%
And, Time (t) = 5 years
Thus, Amount (A)
= $3650 + ($3650 × 3% × 5)
= $3650 + ($3650 ×3/100 × 5)
= $3650 + (3650 × 3 × 5/100)
= $3650 + (10950 × 5/100)
= $3650 + (54750/100)
= $3650 + $547.5 = $4197.5
Thus, Amount (A) to be paid = $4197.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3650, the simple interest in 1 year
= 3/100 × 3650
= 3 × 3650/100
= 10950/100 = $109.5
Thus, simple interest for 1 year = $109.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $109.5 × 5 = $547.5
Thus, Simple Interest (SI) = $547.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $547.5
= $4197.5
Thus, Amount to be paid = $4197.5 Answer
Similar Questions
(1) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?
(2) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(4) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?
(5) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(6) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?
(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(10) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.