Question:
Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
Correct Answer
$3782
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 6%
Time (t) = 4 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% × 4
= $3050 ×6/100 × 4
= 3050 × 6 × 4/100
= 18300 × 4/100
= 73200/100
= $732
Thus, Simple Interest = $732
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 + $732
= $3782
Thus, Amount to be paid = $3782 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) = 4 years
Thus, Amount (A)
= $3050 + ($3050 × 6% × 4)
= $3050 + ($3050 ×6/100 × 4)
= $3050 + (3050 × 6 × 4/100)
= $3050 + (18300 × 4/100)
= $3050 + (73200/100)
= $3050 + $732 = $3782
Thus, Amount (A) to be paid = $3782 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 4 years
= Simple interest for 1 year × 4
= $183 × 4 = $732
Thus, Simple Interest (SI) = $732
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $732
= $3782
Thus, Amount to be paid = $3782 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.
(3) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(5) William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?
(8) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.
(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?