Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.
Correct Answer
$7474
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5050 ×6/100 × 8
= 5050 × 6 × 8/100
= 30300 × 8/100
= 242400/100
= $2424
Thus, Simple Interest = $2424
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 + $2424
= $7474
Thus, Amount to be paid = $7474 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 6% × 8)
= $5050 + ($5050 ×6/100 × 8)
= $5050 + (5050 × 6 × 8/100)
= $5050 + (30300 × 8/100)
= $5050 + (242400/100)
= $5050 + $2424 = $7474
Thus, Amount (A) to be paid = $7474 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5050, the simple interest in 1 year
= 6/100 × 5050
= 6 × 5050/100
= 30300/100 = $303
Thus, simple interest for 1 year = $303
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $303 × 8 = $2424
Thus, Simple Interest (SI) = $2424
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $2424
= $7474
Thus, Amount to be paid = $7474 Answer
Similar Questions
(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(2) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(3) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?
(6) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(8) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.
(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?