Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
Correct Answer
$6844
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 2%
Time (t) = 8 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% × 8
= $5900 ×2/100 × 8
= 5900 × 2 × 8/100
= 11800 × 8/100
= 94400/100
= $944
Thus, Simple Interest = $944
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 + $944
= $6844
Thus, Amount to be paid = $6844 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) = 8 years
Thus, Amount (A)
= $5900 + ($5900 × 2% × 8)
= $5900 + ($5900 ×2/100 × 8)
= $5900 + (5900 × 2 × 8/100)
= $5900 + (11800 × 8/100)
= $5900 + (94400/100)
= $5900 + $944 = $6844
Thus, Amount (A) to be paid = $6844 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 8 years
= Simple interest for 1 year × 8
= $118 × 8 = $944
Thus, Simple Interest (SI) = $944
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $944
= $6844
Thus, Amount to be paid = $6844 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?
(3) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(6) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
(8) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(10) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?