Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 8 years.
Correct Answer
$8436
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5700 ×6/100 × 8
= 5700 × 6 × 8/100
= 34200 × 8/100
= 273600/100
= $2736
Thus, Simple Interest = $2736
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 + $2736
= $8436
Thus, Amount to be paid = $8436 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 6% × 8)
= $5700 + ($5700 ×6/100 × 8)
= $5700 + (5700 × 6 × 8/100)
= $5700 + (34200 × 8/100)
= $5700 + (273600/100)
= $5700 + $2736 = $8436
Thus, Amount (A) to be paid = $8436 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5700, the simple interest in 1 year
= 6/100 × 5700
= 6 × 5700/100
= 34200/100 = $342
Thus, simple interest for 1 year = $342
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $342 × 8 = $2736
Thus, Simple Interest (SI) = $2736
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $2736
= $8436
Thus, Amount to be paid = $8436 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?
(5) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.
(6) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.
(7) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(8) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.
(10) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?