Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?
Correct Answer
$4030
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 6%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 5
= $3100 ×6/100 × 5
= 3100 × 6 × 5/100
= 18600 × 5/100
= 93000/100
= $930
Thus, Simple Interest = $930
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 + $930
= $4030
Thus, Amount to be paid = $4030 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) = 6%
And, Time (t) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 6% × 5)
= $3100 + ($3100 ×6/100 × 5)
= $3100 + (3100 × 6 × 5/100)
= $3100 + (18600 × 5/100)
= $3100 + (93000/100)
= $3100 + $930 = $4030
Thus, Amount (A) to be paid = $4030 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3100, the simple interest in 1 year
= 6/100 × 3100
= 6 × 3100/100
= 18600/100 = $186
Thus, simple interest for 1 year = $186
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $186 × 5 = $930
Thus, Simple Interest (SI) = $930
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $930
= $4030
Thus, Amount to be paid = $4030 Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.
(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.
(5) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?
(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(9) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.