Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
Correct Answer
$7725
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 5%
Time (t) = 10 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) = $5150 × 5% × 10
= $5150 ×5/100 × 10
= 5150 × 5 × 10/100
= 25750 × 10/100
= 257500/100
= $2575
Thus, Simple Interest = $2575
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 = $5150 + $2575
= $7725
Thus, Amount to be paid = $7725 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 = $5150
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 5% × 10)
= $5150 + ($5150 ×5/100 × 10)
= $5150 + (5150 × 5 × 10/100)
= $5150 + (25750 × 10/100)
= $5150 + (257500/100)
= $5150 + $2575 = $7725
Thus, Amount (A) to be paid = $7725 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 $5150, the simple interest in 1 year
= 5/100 × 5150
= 5 × 5150/100
= 25750/100 = $257.5
Thus, simple interest for 1 year = $257.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $257.5 × 10 = $2575
Thus, Simple Interest (SI) = $2575
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2575
= $7725
Thus, Amount to be paid = $7725 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.
(2) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?
(3) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(4) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(5) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 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 7% simple interest for 8 years.
(7) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(8) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(9) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.