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) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.
(3) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(4) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?
(7) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(8) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?
(9) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.
(10) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.