Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.
Correct Answer
$6666
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 8
= $5050 ×4/100 × 8
= 5050 × 4 × 8/100
= 20200 × 8/100
= 161600/100
= $1616
Thus, Simple Interest = $1616
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 + $1616
= $6666
Thus, Amount to be paid = $6666 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) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 4% × 8)
= $5050 + ($5050 ×4/100 × 8)
= $5050 + (5050 × 4 × 8/100)
= $5050 + (20200 × 8/100)
= $5050 + (161600/100)
= $5050 + $1616 = $6666
Thus, Amount (A) to be paid = $6666 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5050, the simple interest in 1 year
= 4/100 × 5050
= 4 × 5050/100
= 20200/100 = $202
Thus, simple interest for 1 year = $202
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $202 × 8 = $1616
Thus, Simple Interest (SI) = $1616
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $1616
= $6666
Thus, Amount to be paid = $6666 Answer
Similar Questions
(1) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?
(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 10% simple interest?
(5) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?
(7) Jennifer had to pay $3445 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 4 years.
(10) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.