Question:
What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?
Correct Answer
$4473
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 7%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 6
= $3150 ×7/100 × 6
= 3150 × 7 × 6/100
= 22050 × 6/100
= 132300/100
= $1323
Thus, Simple Interest = $1323
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 + $1323
= $4473
Thus, Amount to be paid = $4473 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) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3150 + ($3150 × 7% × 6)
= $3150 + ($3150 ×7/100 × 6)
= $3150 + (3150 × 7 × 6/100)
= $3150 + (22050 × 6/100)
= $3150 + (132300/100)
= $3150 + $1323 = $4473
Thus, Amount (A) to be paid = $4473 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3150, the simple interest in 1 year
= 7/100 × 3150
= 7 × 3150/100
= 22050/100 = $220.5
Thus, simple interest for 1 year = $220.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $220.5 × 6 = $1323
Thus, Simple Interest (SI) = $1323
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $1323
= $4473
Thus, Amount to be paid = $4473 Answer
Similar Questions
(1) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?
(2) If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(5) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(8) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.