Question:
What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?
Correct Answer
$4312.5
Solution And Explanation
Solution
Given,
Principal (P) = $3450
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) = $3450 × 5% × 5
= $3450 ×5/100 × 5
= 3450 × 5 × 5/100
= 17250 × 5/100
= 86250/100
= $862.5
Thus, Simple Interest = $862.5
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 + $862.5
= $4312.5
Thus, Amount to be paid = $4312.5 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) = 5%
And, Time (t) = 5 years
Thus, Amount (A)
= $3450 + ($3450 × 5% × 5)
= $3450 + ($3450 ×5/100 × 5)
= $3450 + (3450 × 5 × 5/100)
= $3450 + (17250 × 5/100)
= $3450 + (86250/100)
= $3450 + $862.5 = $4312.5
Thus, Amount (A) to be paid = $4312.5 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 $3450, the simple interest in 1 year
= 5/100 × 3450
= 5 × 3450/100
= 17250/100 = $172.5
Thus, simple interest for 1 year = $172.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $172.5 × 5 = $862.5
Thus, Simple Interest (SI) = $862.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $862.5
= $4312.5
Thus, Amount to be paid = $4312.5 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(3) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(4) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(8) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?
(9) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.