Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 8 years.
Correct Answer
$7980
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5700 ×5/100 × 8
= 5700 × 5 × 8/100
= 28500 × 8/100
= 228000/100
= $2280
Thus, Simple Interest = $2280
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 + $2280
= $7980
Thus, Amount to be paid = $7980 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 5% × 8)
= $5700 + ($5700 ×5/100 × 8)
= $5700 + (5700 × 5 × 8/100)
= $5700 + (28500 × 8/100)
= $5700 + (228000/100)
= $5700 + $2280 = $7980
Thus, Amount (A) to be paid = $7980 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5700, the simple interest in 1 year
= 5/100 × 5700
= 5 × 5700/100
= 28500/100 = $285
Thus, simple interest for 1 year = $285
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $285 × 8 = $2280
Thus, Simple Interest (SI) = $2280
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $2280
= $7980
Thus, Amount to be paid = $7980 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(2) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(4) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
(7) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) 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.
(9) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(10) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?