Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.
Correct Answer
$6962
Solution And Explanation
Solution
Given,
Principal (P) = $5900
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) = $5900 × 2% × 9
= $5900 ×2/100 × 9
= 5900 × 2 × 9/100
= 11800 × 9/100
= 106200/100
= $1062
Thus, Simple Interest = $1062
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 = $5900 + $1062
= $6962
Thus, Amount to be paid = $6962 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 = $5900
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 2% × 9)
= $5900 + ($5900 ×2/100 × 9)
= $5900 + (5900 × 2 × 9/100)
= $5900 + (11800 × 9/100)
= $5900 + (106200/100)
= $5900 + $1062 = $6962
Thus, Amount (A) to be paid = $6962 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 $5900, the simple interest in 1 year
= 2/100 × 5900
= 2 × 5900/100
= 11800/100 = $118
Thus, simple interest for 1 year = $118
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $118 × 9 = $1062
Thus, Simple Interest (SI) = $1062
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $1062
= $6962
Thus, Amount to be paid = $6962 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(2) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(3) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?
(4) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(5) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(7) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(8) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(9) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?