Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.
Correct Answer
$7622
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5150 ×6/100 × 8
= 5150 × 6 × 8/100
= 30900 × 8/100
= 247200/100
= $2472
Thus, Simple Interest = $2472
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 + $2472
= $7622
Thus, Amount to be paid = $7622 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 6% × 8)
= $5150 + ($5150 ×6/100 × 8)
= $5150 + (5150 × 6 × 8/100)
= $5150 + (30900 × 8/100)
= $5150 + (247200/100)
= $5150 + $2472 = $7622
Thus, Amount (A) to be paid = $7622 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5150, the simple interest in 1 year
= 6/100 × 5150
= 6 × 5150/100
= 30900/100 = $309
Thus, simple interest for 1 year = $309
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $309 × 8 = $2472
Thus, Simple Interest (SI) = $2472
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2472
= $7622
Thus, Amount to be paid = $7622 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(3) In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?
(4) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?
(5) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?
(6) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.
(7) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(8) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.