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) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(4) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(7) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(9) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.