Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
Correct Answer
$6262
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $5050 × 3% × 8
= $5050 ×3/100 × 8
= 5050 × 3 × 8/100
= 15150 × 8/100
= 121200/100
= $1212
Thus, Simple Interest = $1212
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 = $5050 + $1212
= $6262
Thus, Amount to be paid = $6262 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 = $5050
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 3% × 8)
= $5050 + ($5050 ×3/100 × 8)
= $5050 + (5050 × 3 × 8/100)
= $5050 + (15150 × 8/100)
= $5050 + (121200/100)
= $5050 + $1212 = $6262
Thus, Amount (A) to be paid = $6262 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5050, the simple interest in 1 year
= 3/100 × 5050
= 3 × 5050/100
= 15150/100 = $151.5
Thus, simple interest for 1 year = $151.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $151.5 × 8 = $1212
Thus, Simple Interest (SI) = $1212
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $1212
= $6262
Thus, Amount to be paid = $6262 Answer
Similar Questions
(1) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(2) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?
(3) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(4) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(5) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.
(7) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.
(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?