Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.
Correct Answer
$5974
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 2%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5150 × 2% × 8
= $5150 ×2/100 × 8
= 5150 × 2 × 8/100
= 10300 × 8/100
= 82400/100
= $824
Thus, Simple Interest = $824
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 = $5150 + $824
= $5974
Thus, Amount to be paid = $5974 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 = $5150
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 2% × 8)
= $5150 + ($5150 ×2/100 × 8)
= $5150 + (5150 × 2 × 8/100)
= $5150 + (10300 × 8/100)
= $5150 + (82400/100)
= $5150 + $824 = $5974
Thus, Amount (A) to be paid = $5974 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5150, the simple interest in 1 year
= 2/100 × 5150
= 2 × 5150/100
= 10300/100 = $103
Thus, simple interest for 1 year = $103
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $103 × 8 = $824
Thus, Simple Interest (SI) = $824
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $824
= $5974
Thus, Amount to be paid = $5974 Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 2% simple interest?
(2) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(3) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.
(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?
(9) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 7 years.
(10) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.