Question:
Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.
Correct Answer
$6600
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5000 × 4% × 8
= $5000 ×4/100 × 8
= 5000 × 4 × 8/100
= 20000 × 8/100
= 160000/100
= $1600
Thus, Simple Interest = $1600
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 = $5000 + $1600
= $6600
Thus, Amount to be paid = $6600 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 = $5000
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5000 + ($5000 × 4% × 8)
= $5000 + ($5000 ×4/100 × 8)
= $5000 + (5000 × 4 × 8/100)
= $5000 + (20000 × 8/100)
= $5000 + (160000/100)
= $5000 + $1600 = $6600
Thus, Amount (A) to be paid = $6600 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5000, the simple interest in 1 year
= 4/100 × 5000
= 4 × 5000/100
= 20000/100 = $200
Thus, simple interest for 1 year = $200
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $200 × 8 = $1600
Thus, Simple Interest (SI) = $1600
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $1600
= $6600
Thus, Amount to be paid = $6600 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(2) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(3) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(4) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
(6) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
(10) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.