Question:
If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3339
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 3%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 2
= $3150 ×3/100 × 2
= 3150 × 3 × 2/100
= 9450 × 2/100
= 18900/100
= $189
Thus, Simple Interest = $189
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 + $189
= $3339
Thus, Amount to be paid = $3339 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) = 3%
And, Time (t) = 2 years
Thus, Amount (A)
= $3150 + ($3150 × 3% × 2)
= $3150 + ($3150 ×3/100 × 2)
= $3150 + (3150 × 3 × 2/100)
= $3150 + (9450 × 2/100)
= $3150 + (18900/100)
= $3150 + $189 = $3339
Thus, Amount (A) to be paid = $3339 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3150, the simple interest in 1 year
= 3/100 × 3150
= 3 × 3150/100
= 9450/100 = $94.5
Thus, simple interest for 1 year = $94.5
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $94.5 × 2 = $189
Thus, Simple Interest (SI) = $189
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $189
= $3339
Thus, Amount to be paid = $3339 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(2) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?
(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.
(8) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
(9) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(10) 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.