Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.
Correct Answer
$3720
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 5%
Time (t) = 4 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) = $3100 × 5% × 4
= $3100 ×5/100 × 4
= 3100 × 5 × 4/100
= 15500 × 4/100
= 62000/100
= $620
Thus, Simple Interest = $620
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 + $620
= $3720
Thus, Amount to be paid = $3720 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) = 5%
And, Time (t) = 4 years
Thus, Amount (A)
= $3100 + ($3100 × 5% × 4)
= $3100 + ($3100 ×5/100 × 4)
= $3100 + (3100 × 5 × 4/100)
= $3100 + (15500 × 4/100)
= $3100 + (62000/100)
= $3100 + $620 = $3720
Thus, Amount (A) to be paid = $3720 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 $3100, the simple interest in 1 year
= 5/100 × 3100
= 5 × 3100/100
= 15500/100 = $155
Thus, simple interest for 1 year = $155
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $155 × 4 = $620
Thus, Simple Interest (SI) = $620
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $620
= $3720
Thus, Amount to be paid = $3720 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(3) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(4) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
(8) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.