Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.
Correct Answer
$3967.5
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 5%
Time (t) = 3 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% × 3
= $3450 ×5/100 × 3
= 3450 × 5 × 3/100
= 17250 × 3/100
= 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) = 5%
And, Time (t) = 3 years
Thus, Amount (A)
= $3450 + ($3450 × 5% × 3)
= $3450 + ($3450 ×5/100 × 3)
= $3450 + (3450 × 5 × 3/100)
= $3450 + (17250 × 3/100)
= $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 = 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 3 years
= Simple interest for 1 year × 3
= $172.5 × 3 = $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) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?
(2) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
(5) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(6) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?
(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(8) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(9) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.
(10) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?