Question:
Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.
Correct Answer
$4026
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 8%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 4
= $3050 ×8/100 × 4
= 3050 × 8 × 4/100
= 24400 × 4/100
= 97600/100
= $976
Thus, Simple Interest = $976
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 + $976
= $4026
Thus, Amount to be paid = $4026 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) = 8%
And, Time (t) = 4 years
Thus, Amount (A)
= $3050 + ($3050 × 8% × 4)
= $3050 + ($3050 ×8/100 × 4)
= $3050 + (3050 × 8 × 4/100)
= $3050 + (24400 × 4/100)
= $3050 + (97600/100)
= $3050 + $976 = $4026
Thus, Amount (A) to be paid = $4026 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3050, the simple interest in 1 year
= 8/100 × 3050
= 8 × 3050/100
= 24400/100 = $244
Thus, simple interest for 1 year = $244
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $244 × 4 = $976
Thus, Simple Interest (SI) = $976
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $976
= $4026
Thus, Amount to be paid = $4026 Answer
Similar Questions
(1) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(2) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(3) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?
(5) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?
(7) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?
(8) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?
(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?
(10) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.