Question:
What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?
Correct Answer
$4725
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 10%
Time (t) = 5 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% × 5
= $3150 ×10/100 × 5
= 3150 × 10 × 5/100
= 31500 × 5/100
= 157500/100
= $1575
Thus, Simple Interest = $1575
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 + $1575
= $4725
Thus, Amount to be paid = $4725 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) = 5 years
Thus, Amount (A)
= $3150 + ($3150 × 10% × 5)
= $3150 + ($3150 ×10/100 × 5)
= $3150 + (3150 × 10 × 5/100)
= $3150 + (31500 × 5/100)
= $3150 + (157500/100)
= $3150 + $1575 = $4725
Thus, Amount (A) to be paid = $4725 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 5 years
= Simple interest for 1 year × 5
= $315 × 5 = $1575
Thus, Simple Interest (SI) = $1575
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $1575
= $4725
Thus, Amount to be paid = $4725 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.
(3) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 4 years.
(4) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.
(5) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.
(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(9) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?