Question:
What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 6% simple interest?
Correct Answer
$4148
Solution And Explanation
Solution
Given,
Principal (P) = $3050
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) = $3050 × 6% × 6
= $3050 ×6/100 × 6
= 3050 × 6 × 6/100
= 18300 × 6/100
= 109800/100
= $1098
Thus, Simple Interest = $1098
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 = $3050 + $1098
= $4148
Thus, Amount to be paid = $4148 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 = $3050
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 6 years
Thus, Amount (A)
= $3050 + ($3050 × 6% × 6)
= $3050 + ($3050 ×6/100 × 6)
= $3050 + (3050 × 6 × 6/100)
= $3050 + (18300 × 6/100)
= $3050 + (109800/100)
= $3050 + $1098 = $4148
Thus, Amount (A) to be paid = $4148 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 $3050, the simple interest in 1 year
= 6/100 × 3050
= 6 × 3050/100
= 18300/100 = $183
Thus, simple interest for 1 year = $183
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $183 × 6 = $1098
Thus, Simple Interest (SI) = $1098
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $1098
= $4148
Thus, Amount to be paid = $4148 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(2) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.
(3) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?
(4) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.
(5) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?
(6) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
(9) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
(10) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.