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) How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.
(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(5) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(6) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) If Jennifer paid $3510 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.
(9) 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.
(10) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.