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) If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.
(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
(5) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(7) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.
(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?