Question:
Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 4 years.
Correct Answer
$3538
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 4%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 4
= $3050 ×4/100 × 4
= 3050 × 4 × 4/100
= 12200 × 4/100
= 48800/100
= $488
Thus, Simple Interest = $488
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 + $488
= $3538
Thus, Amount to be paid = $3538 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) = 4%
And, Time (t) = 4 years
Thus, Amount (A)
= $3050 + ($3050 × 4% × 4)
= $3050 + ($3050 ×4/100 × 4)
= $3050 + (3050 × 4 × 4/100)
= $3050 + (12200 × 4/100)
= $3050 + (48800/100)
= $3050 + $488 = $3538
Thus, Amount (A) to be paid = $3538 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3050, the simple interest in 1 year
= 4/100 × 3050
= 4 × 3050/100
= 12200/100 = $122
Thus, simple interest for 1 year = $122
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $122 × 4 = $488
Thus, Simple Interest (SI) = $488
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $488
= $3538
Thus, Amount to be paid = $3538 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 3 years.
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.
(4) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.
(6) If Joseph paid $4144 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(8) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(9) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.