Question:
What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
Correct Answer
$3812.5
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 5%
Time (t) = 5 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% × 5
= $3050 ×5/100 × 5
= 3050 × 5 × 5/100
= 15250 × 5/100
= 76250/100
= $762.5
Thus, Simple Interest = $762.5
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 + $762.5
= $3812.5
Thus, Amount to be paid = $3812.5 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) = 5 years
Thus, Amount (A)
= $3050 + ($3050 × 5% × 5)
= $3050 + ($3050 ×5/100 × 5)
= $3050 + (3050 × 5 × 5/100)
= $3050 + (15250 × 5/100)
= $3050 + (76250/100)
= $3050 + $762.5 = $3812.5
Thus, Amount (A) to be paid = $3812.5 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 5 years
= Simple interest for 1 year × 5
= $152.5 × 5 = $762.5
Thus, Simple Interest (SI) = $762.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $762.5
= $3812.5
Thus, Amount to be paid = $3812.5 Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.
(2) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?
(3) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?
(5) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.
(7) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?
(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.