Question

If you want to earn 4% annual simple interest on an investment, how much should you pay for a note that will be worth $17,500 in 10 months?

Answer 1

Answer: $16,936

Step-by-step explanation:

Formula for simple interest :

$I=P\cdot r\cdot t$            (1)

, where P = Principal amount.

r= rate of interest ( in decimal)

t= time

Future value : A= P+I  

or I=A-P            (2)

Given : r= 4% = 0.04

Time = 10 months = $\dfrac{10}{12}$ year  [∵ 1 year = 12 months]

Then, from (1), we have

Simple interest :$I=P\cdot (0.04)\cdot \dfrac{10}{12}=0.0333P$            (3)

Future value : A=  $17,500

Let P be the initial amount needed to invest .

Then from(2), we have

Simple interest : I= $17,500-P               (4)

From  (3) and (4), we have

$0.0333P=17500-P\\\\\Rightarrow\ 0.0333P+P=17500\\\\\Rightarrow\  1.0333P=17500\\\\\Rightarrow\ P=\dfrac{17500}{1.0333}\approx16,936$

Hence, you should pay $16,936 for a note that will be worth $17,500 in 10 months.

Answer 2

The amount you should pay for a note is $16,935.48.

What is simple interest?

Simple interest is interest that is only paid on the amount invested.

Amount = interest / (time x interest rate)

Let x represent the amount

x = 17,500 - x / (0.04 x 10/12)

x =  17,500 - x / 0.0333

0.033x =  17,500 - x

1.033x = 17500

x = 17500 / 1.0333

x = $16,935.48

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