Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.
Correct Answer
$4092
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 8%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $3100 × 8% × 4
= $3100 ×8/100 × 4
= 3100 × 8 × 4/100
= 24800 × 4/100
= 99200/100
= $992
Thus, Simple Interest = $992
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 = $3100 + $992
= $4092
Thus, Amount to be paid = $4092 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 = $3100
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 4 years
Thus, Amount (A)
= $3100 + ($3100 × 8% × 4)
= $3100 + ($3100 ×8/100 × 4)
= $3100 + (3100 × 8 × 4/100)
= $3100 + (24800 × 4/100)
= $3100 + (99200/100)
= $3100 + $992 = $4092
Thus, Amount (A) to be paid = $4092 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3100, the simple interest in 1 year
= 8/100 × 3100
= 8 × 3100/100
= 24800/100 = $248
Thus, simple interest for 1 year = $248
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $248 × 4 = $992
Thus, Simple Interest (SI) = $992
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $992
= $4092
Thus, Amount to be paid = $4092 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.
(2) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?
(4) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(6) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(7) 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.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.
(9) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.
(10) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?