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) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(3) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 3% simple interest?
(4) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.
(5) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(6) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?
(7) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?
(9) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?