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) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?
(3) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 7 years.
(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.
(7) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(8) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?
(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) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.