Question:
What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
Correct Answer
$4095
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 5%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 6
= $3150 ×5/100 × 6
= 3150 × 5 × 6/100
= 15750 × 6/100
= 94500/100
= $945
Thus, Simple Interest = $945
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 + $945
= $4095
Thus, Amount to be paid = $4095 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) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3150 + ($3150 × 5% × 6)
= $3150 + ($3150 ×5/100 × 6)
= $3150 + (3150 × 5 × 6/100)
= $3150 + (15750 × 6/100)
= $3150 + (94500/100)
= $3150 + $945 = $4095
Thus, Amount (A) to be paid = $4095 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3150, the simple interest in 1 year
= 5/100 × 3150
= 5 × 3150/100
= 15750/100 = $157.5
Thus, simple interest for 1 year = $157.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $157.5 × 6 = $945
Thus, Simple Interest (SI) = $945
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $945
= $4095
Thus, Amount to be paid = $4095 Answer
Similar Questions
(1) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.
(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?
(6) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.
(7) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.
(9) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?