Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
Correct Answer
$8772
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5100 × 8% × 9
= $5100 ×8/100 × 9
= 5100 × 8 × 9/100
= 40800 × 9/100
= 367200/100
= $3672
Thus, Simple Interest = $3672
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 = $5100 + $3672
= $8772
Thus, Amount to be paid = $8772 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 = $5100
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 8% × 9)
= $5100 + ($5100 ×8/100 × 9)
= $5100 + (5100 × 8 × 9/100)
= $5100 + (40800 × 9/100)
= $5100 + (367200/100)
= $5100 + $3672 = $8772
Thus, Amount (A) to be paid = $8772 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5100, the simple interest in 1 year
= 8/100 × 5100
= 8 × 5100/100
= 40800/100 = $408
Thus, simple interest for 1 year = $408
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $408 × 9 = $3672
Thus, Simple Interest (SI) = $3672
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $3672
= $8772
Thus, Amount to be paid = $8772 Answer
Similar Questions
(1) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(4) 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?
(5) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.
(6) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(8) How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?
(9) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.
(10) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?