Question:
What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?
Correct Answer
$4095
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 6%
Time (t) = 5 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) = $3150 × 6% × 5
= $3150 ×6/100 × 5
= 3150 × 6 × 5/100
= 18900 × 5/100
= 94500/100
= $945
Thus, Simple Interest = $945
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 = $3150 + $945
= $4095
Thus, Amount to be paid = $4095 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 = $3150
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 5 years
Thus, Amount (A)
= $3150 + ($3150 × 6% × 5)
= $3150 + ($3150 ×6/100 × 5)
= $3150 + (3150 × 6 × 5/100)
= $3150 + (18900 × 5/100)
= $3150 + (94500/100)
= $3150 + $945 = $4095
Thus, Amount (A) to be paid = $4095 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 $3150, the simple interest in 1 year
= 6/100 × 3150
= 6 × 3150/100
= 18900/100 = $189
Thus, simple interest for 1 year = $189
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $189 × 5 = $945
Thus, Simple Interest (SI) = $945
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $945
= $4095
Thus, Amount to be paid = $4095 Answer
Similar Questions
(1) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(3) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?
(4) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?
(8) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(10) How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?