Question:
What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
Correct Answer
$4216
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 6%
Time (t) = 6 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% × 6
= $3100 ×6/100 × 6
= 3100 × 6 × 6/100
= 18600 × 6/100
= 111600/100
= $1116
Thus, Simple Interest = $1116
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 + $1116
= $4216
Thus, Amount to be paid = $4216 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) = 6 years
Thus, Amount (A)
= $3100 + ($3100 × 6% × 6)
= $3100 + ($3100 ×6/100 × 6)
= $3100 + (3100 × 6 × 6/100)
= $3100 + (18600 × 6/100)
= $3100 + (111600/100)
= $3100 + $1116 = $4216
Thus, Amount (A) to be paid = $4216 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 6 years
= Simple interest for 1 year × 6
= $186 × 6 = $1116
Thus, Simple Interest (SI) = $1116
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1116
= $4216
Thus, Amount to be paid = $4216 Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.
(2) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?
(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?
(5) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11765 to clear the loan, then find the time period of the loan.
(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(7) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.
(10) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.