Question:
What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?
Correct Answer
$4657.5
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 7%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $3450 × 7% × 5
= $3450 ×7/100 × 5
= 3450 × 7 × 5/100
= 24150 × 5/100
= 120750/100
= $1207.5
Thus, Simple Interest = $1207.5
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 = $3450 + $1207.5
= $4657.5
Thus, Amount to be paid = $4657.5 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 = $3450
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 5 years
Thus, Amount (A)
= $3450 + ($3450 × 7% × 5)
= $3450 + ($3450 ×7/100 × 5)
= $3450 + (3450 × 7 × 5/100)
= $3450 + (24150 × 5/100)
= $3450 + (120750/100)
= $3450 + $1207.5 = $4657.5
Thus, Amount (A) to be paid = $4657.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3450, the simple interest in 1 year
= 7/100 × 3450
= 7 × 3450/100
= 24150/100 = $241.5
Thus, simple interest for 1 year = $241.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $241.5 × 5 = $1207.5
Thus, Simple Interest (SI) = $1207.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1207.5
= $4657.5
Thus, Amount to be paid = $4657.5 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(2) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?
(3) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.
(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?
(6) If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?
(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(9) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?