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 Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?
(2) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.
(3) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?
(4) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.
(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?
(7) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.
(9) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?
(10) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?