Question:
What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?
Correct Answer
$4270
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 8%
Time (t) = 5 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% × 5
= $3050 ×8/100 × 5
= 3050 × 8 × 5/100
= 24400 × 5/100
= 122000/100
= $1220
Thus, Simple Interest = $1220
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 + $1220
= $4270
Thus, Amount to be paid = $4270 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) = 5 years
Thus, Amount (A)
= $3050 + ($3050 × 8% × 5)
= $3050 + ($3050 ×8/100 × 5)
= $3050 + (3050 × 8 × 5/100)
= $3050 + (24400 × 5/100)
= $3050 + (122000/100)
= $3050 + $1220 = $4270
Thus, Amount (A) to be paid = $4270 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 5 years
= Simple interest for 1 year × 5
= $244 × 5 = $1220
Thus, Simple Interest (SI) = $1220
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $1220
= $4270
Thus, Amount to be paid = $4270 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.
(3) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(4) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?
(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(9) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.