Question:
What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?
Correct Answer
$3780
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 4%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 5
= $3150 ×4/100 × 5
= 3150 × 4 × 5/100
= 12600 × 5/100
= 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) = 4%
And, Time (t) = 5 years
Thus, Amount (A)
= $3150 + ($3150 × 4% × 5)
= $3150 + ($3150 ×4/100 × 5)
= $3150 + (3150 × 4 × 5/100)
= $3150 + (12600 × 5/100)
= $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 = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3150, the simple interest in 1 year
= 4/100 × 3150
= 4 × 3150/100
= 12600/100 = $126
Thus, simple interest for 1 year = $126
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $126 × 5 = $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) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(3) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(4) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(5) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?
(7) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?
(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?
(9) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.