Question:
What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
Correct Answer
$4095
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 5%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 6
= $3150 ×5/100 × 6
= 3150 × 5 × 6/100
= 15750 × 6/100
= 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) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3150 + ($3150 × 5% × 6)
= $3150 + ($3150 ×5/100 × 6)
= $3150 + (3150 × 5 × 6/100)
= $3150 + (15750 × 6/100)
= $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 = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3150, the simple interest in 1 year
= 5/100 × 3150
= 5 × 3150/100
= 15750/100 = $157.5
Thus, simple interest for 1 year = $157.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $157.5 × 6 = $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) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?
(6) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.
(7) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.
(10) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?