Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?
Correct Answer
$3875
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 5%
Time (t) = 5 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% × 5
= $3100 ×5/100 × 5
= 3100 × 5 × 5/100
= 15500 × 5/100
= 77500/100
= $775
Thus, Simple Interest = $775
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 + $775
= $3875
Thus, Amount to be paid = $3875 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) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 5% × 5)
= $3100 + ($3100 ×5/100 × 5)
= $3100 + (3100 × 5 × 5/100)
= $3100 + (15500 × 5/100)
= $3100 + (77500/100)
= $3100 + $775 = $3875
Thus, Amount (A) to be paid = $3875 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 5 years
= Simple interest for 1 year × 5
= $155 × 5 = $775
Thus, Simple Interest (SI) = $775
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $775
= $3875
Thus, Amount to be paid = $3875 Answer
Similar Questions
(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(2) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
(4) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
(5) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.
(6) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(10) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?