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 Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?
(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?
(3) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(4) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.
(6) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 10% simple interest?
(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?
(9) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(10) How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?