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) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?
(2) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.
(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(7) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(9) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.