Question:
What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
Correct Answer
$3967.5
Solution And Explanation
Solution
Given,
Principal (P) = $3450
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) = $3450 × 3% × 5
= $3450 ×3/100 × 5
= 3450 × 3 × 5/100
= 10350 × 5/100
= 51750/100
= $517.5
Thus, Simple Interest = $517.5
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 + $517.5
= $3967.5
Thus, Amount to be paid = $3967.5 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) = 3%
And, Time (t) = 5 years
Thus, Amount (A)
= $3450 + ($3450 × 3% × 5)
= $3450 + ($3450 ×3/100 × 5)
= $3450 + (3450 × 3 × 5/100)
= $3450 + (10350 × 5/100)
= $3450 + (51750/100)
= $3450 + $517.5 = $3967.5
Thus, Amount (A) to be paid = $3967.5 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 $3450, the simple interest in 1 year
= 3/100 × 3450
= 3 × 3450/100
= 10350/100 = $103.5
Thus, simple interest for 1 year = $103.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $103.5 × 5 = $517.5
Thus, Simple Interest (SI) = $517.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $517.5
= $3967.5
Thus, Amount to be paid = $3967.5 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(3) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.
(5) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(7) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
(9) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(10) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.