Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.
Correct Answer
$6148
Solution And Explanation
Solution
Given,
Principal (P) = $5300
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) = $5300 × 2% × 8
= $5300 ×2/100 × 8
= 5300 × 2 × 8/100
= 10600 × 8/100
= 84800/100
= $848
Thus, Simple Interest = $848
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 = $5300 + $848
= $6148
Thus, Amount to be paid = $6148 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 = $5300
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 2% × 8)
= $5300 + ($5300 ×2/100 × 8)
= $5300 + (5300 × 2 × 8/100)
= $5300 + (10600 × 8/100)
= $5300 + (84800/100)
= $5300 + $848 = $6148
Thus, Amount (A) to be paid = $6148 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 $5300, the simple interest in 1 year
= 2/100 × 5300
= 2 × 5300/100
= 10600/100 = $106
Thus, simple interest for 1 year = $106
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $106 × 8 = $848
Thus, Simple Interest (SI) = $848
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $848
= $6148
Thus, Amount to be paid = $6148 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.
(3) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(4) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?
(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) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?
(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?