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) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.
(3) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.
(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(7) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
(8) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?
(10) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.