Question:
Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
Correct Answer
$6726
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 2%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5700 × 2% × 9
= $5700 ×2/100 × 9
= 5700 × 2 × 9/100
= 11400 × 9/100
= 102600/100
= $1026
Thus, Simple Interest = $1026
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 = $5700 + $1026
= $6726
Thus, Amount to be paid = $6726 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 = $5700
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5700 + ($5700 × 2% × 9)
= $5700 + ($5700 ×2/100 × 9)
= $5700 + (5700 × 2 × 9/100)
= $5700 + (11400 × 9/100)
= $5700 + (102600/100)
= $5700 + $1026 = $6726
Thus, Amount (A) to be paid = $6726 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5700, the simple interest in 1 year
= 2/100 × 5700
= 2 × 5700/100
= 11400/100 = $114
Thus, simple interest for 1 year = $114
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $114 × 9 = $1026
Thus, Simple Interest (SI) = $1026
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1026
= $6726
Thus, Amount to be paid = $6726 Answer
Similar Questions
(1) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.
(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(5) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.
(6) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
(8) How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?
(9) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(10) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.