Question:
What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
Correct Answer
$5175
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 10%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 5
= $3450 ×10/100 × 5
= 3450 × 10 × 5/100
= 34500 × 5/100
= 172500/100
= $1725
Thus, Simple Interest = $1725
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 + $1725
= $5175
Thus, Amount to be paid = $5175 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) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3450 + ($3450 × 10% × 5)
= $3450 + ($3450 ×10/100 × 5)
= $3450 + (3450 × 10 × 5/100)
= $3450 + (34500 × 5/100)
= $3450 + (172500/100)
= $3450 + $1725 = $5175
Thus, Amount (A) to be paid = $5175 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3450, the simple interest in 1 year
= 10/100 × 3450
= 10 × 3450/100
= 34500/100 = $345
Thus, simple interest for 1 year = $345
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $345 × 5 = $1725
Thus, Simple Interest (SI) = $1725
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1725
= $5175
Thus, Amount to be paid = $5175 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(2) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 4 years.
(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(5) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?
(6) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(7) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(10) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.