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) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.
(2) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.
(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?
(4) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(8) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(10) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?