Question:
What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?
Correct Answer
$3780
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 10%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $3150 × 10% × 2
= $3150 ×10/100 × 2
= 3150 × 10 × 2/100
= 31500 × 2/100
= 63000/100
= $630
Thus, Simple Interest = $630
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 = $3150 + $630
= $3780
Thus, Amount to be paid = $3780 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 = $3150
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 2 years
Thus, Amount (A)
= $3150 + ($3150 × 10% × 2)
= $3150 + ($3150 ×10/100 × 2)
= $3150 + (3150 × 10 × 2/100)
= $3150 + (31500 × 2/100)
= $3150 + (63000/100)
= $3150 + $630 = $3780
Thus, Amount (A) to be paid = $3780 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3150, the simple interest in 1 year
= 10/100 × 3150
= 10 × 3150/100
= 31500/100 = $315
Thus, simple interest for 1 year = $315
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $315 × 2 = $630
Thus, Simple Interest (SI) = $630
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $630
= $3780
Thus, Amount to be paid = $3780 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.
(4) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.
(9) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.