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) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(2) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(5) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?
(6) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(7) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.
(9) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(10) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?