Question:
Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 4 years.
Correct Answer
$3660
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 5%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 4
= $3050 ×5/100 × 4
= 3050 × 5 × 4/100
= 15250 × 4/100
= 61000/100
= $610
Thus, Simple Interest = $610
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 + $610
= $3660
Thus, Amount to be paid = $3660 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) = 5%
And, Time (t) = 4 years
Thus, Amount (A)
= $3050 + ($3050 × 5% × 4)
= $3050 + ($3050 ×5/100 × 4)
= $3050 + (3050 × 5 × 4/100)
= $3050 + (15250 × 4/100)
= $3050 + (61000/100)
= $3050 + $610 = $3660
Thus, Amount (A) to be paid = $3660 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3050, the simple interest in 1 year
= 5/100 × 3050
= 5 × 3050/100
= 15250/100 = $152.5
Thus, simple interest for 1 year = $152.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $152.5 × 4 = $610
Thus, Simple Interest (SI) = $610
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $610
= $3660
Thus, Amount to be paid = $3660 Answer
Similar Questions
(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(2) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(4) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(6) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.
(8) Barbara had to pay $3976 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
(10) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?