Question:
What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?
Correct Answer
$5476
Solution And Explanation
Solution
Given,
Principal (P) = $3700
Rate of Simple Interest (SI) = 8%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $3700 × 8% × 6
= $3700 ×8/100 × 6
= 3700 × 8 × 6/100
= 29600 × 6/100
= 177600/100
= $1776
Thus, Simple Interest = $1776
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 = $3700 + $1776
= $5476
Thus, Amount to be paid = $5476 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 = $3700
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 6 years
Thus, Amount (A)
= $3700 + ($3700 × 8% × 6)
= $3700 + ($3700 ×8/100 × 6)
= $3700 + (3700 × 8 × 6/100)
= $3700 + (29600 × 6/100)
= $3700 + (177600/100)
= $3700 + $1776 = $5476
Thus, Amount (A) to be paid = $5476 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3700, the simple interest in 1 year
= 8/100 × 3700
= 8 × 3700/100
= 29600/100 = $296
Thus, simple interest for 1 year = $296
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $296 × 6 = $1776
Thus, Simple Interest (SI) = $1776
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3700 + $1776
= $5476
Thus, Amount to be paid = $5476 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(5) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(6) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.
(7) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?
(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.
(9) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.