Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 4 years.
Correct Answer
$4140
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 5%
Time (t) = 4 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% × 4
= $3450 ×5/100 × 4
= 3450 × 5 × 4/100
= 17250 × 4/100
= 69000/100
= $690
Thus, Simple Interest = $690
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 + $690
= $4140
Thus, Amount to be paid = $4140 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) = 4 years
Thus, Amount (A)
= $3450 + ($3450 × 5% × 4)
= $3450 + ($3450 ×5/100 × 4)
= $3450 + (3450 × 5 × 4/100)
= $3450 + (17250 × 4/100)
= $3450 + (69000/100)
= $3450 + $690 = $4140
Thus, Amount (A) to be paid = $4140 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 4 years
= Simple interest for 1 year × 4
= $172.5 × 4 = $690
Thus, Simple Interest (SI) = $690
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $690
= $4140
Thus, Amount to be paid = $4140 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(4) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?
(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(9) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.
(10) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.