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) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
(4) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.
(5) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(7) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
(9) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(10) Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.