Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?
Correct Answer
$4495
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 9%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 5
= $3100 ×9/100 × 5
= 3100 × 9 × 5/100
= 27900 × 5/100
= 139500/100
= $1395
Thus, Simple Interest = $1395
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 + $1395
= $4495
Thus, Amount to be paid = $4495 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) = 9%
And, Time (t) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 9% × 5)
= $3100 + ($3100 ×9/100 × 5)
= $3100 + (3100 × 9 × 5/100)
= $3100 + (27900 × 5/100)
= $3100 + (139500/100)
= $3100 + $1395 = $4495
Thus, Amount (A) to be paid = $4495 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3100, the simple interest in 1 year
= 9/100 × 3100
= 9 × 3100/100
= 27900/100 = $279
Thus, simple interest for 1 year = $279
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $279 × 5 = $1395
Thus, Simple Interest (SI) = $1395
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1395
= $4495
Thus, Amount to be paid = $4495 Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 7 years.
(2) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.
(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.
(5) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(6) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(7) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?
(9) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.