Question:
What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
Correct Answer
$4575
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 10%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 5
= $3050 ×10/100 × 5
= 3050 × 10 × 5/100
= 30500 × 5/100
= 152500/100
= $1525
Thus, Simple Interest = $1525
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 + $1525
= $4575
Thus, Amount to be paid = $4575 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) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3050 + ($3050 × 10% × 5)
= $3050 + ($3050 ×10/100 × 5)
= $3050 + (3050 × 10 × 5/100)
= $3050 + (30500 × 5/100)
= $3050 + (152500/100)
= $3050 + $1525 = $4575
Thus, Amount (A) to be paid = $4575 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3050, the simple interest in 1 year
= 10/100 × 3050
= 10 × 3050/100
= 30500/100 = $305
Thus, simple interest for 1 year = $305
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $305 × 5 = $1525
Thus, Simple Interest (SI) = $1525
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $1525
= $4575
Thus, Amount to be paid = $4575 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.
(4) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(6) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.
(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(9) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(10) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.