Question:
What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?
Correct Answer
$3658
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 3%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 6
= $3100 ×3/100 × 6
= 3100 × 3 × 6/100
= 9300 × 6/100
= 55800/100
= $558
Thus, Simple Interest = $558
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 + $558
= $3658
Thus, Amount to be paid = $3658 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) = 3%
And, Time (t) = 6 years
Thus, Amount (A)
= $3100 + ($3100 × 3% × 6)
= $3100 + ($3100 ×3/100 × 6)
= $3100 + (3100 × 3 × 6/100)
= $3100 + (9300 × 6/100)
= $3100 + (55800/100)
= $3100 + $558 = $3658
Thus, Amount (A) to be paid = $3658 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3100, the simple interest in 1 year
= 3/100 × 3100
= 3 × 3100/100
= 9300/100 = $93
Thus, simple interest for 1 year = $93
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $93 × 6 = $558
Thus, Simple Interest (SI) = $558
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $558
= $3658
Thus, Amount to be paid = $3658 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.
(2) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 4 years.
(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?
(5) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.
(7) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(9) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(10) 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.