Find the compound interest rate equivalent to the simple interest rate of 5% for an investment over a 4 years period

I

itsrayex

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Sorry if the awkward translation but I am directly translating this from another language

Here are the options:
1644778403141.png
I have no idea regarding what formula I should use to solve this, I have made a useless attempt knowing this is not the right way to do it:
1644778499372.png
Can you please tell me what is the solution and why? Thank you
 
Edited: I mixed up the two rates
Let A= the final amount, P= initial amount, i= annual simple interest rate, x= annual compound interest rate, n= time (in years)
The formula for compound interest rate is [imath]A=P(1+x)^n=P(1+x)^4[/imath]
The formula for simple interest rate is [imath]A=P(1+i\cdot n)=P(1+0.05\cdot 4)[/imath]
For the interest rates to be equivalent, the final value has to be the same given the same initial value, so equate the 2 equations and solve for [imath]x[/imath]:
[math]P(1+x)^4=P(1+0.05\cdot 4)[/math]
 
Last edited:
BigBeachBanana said:
Edited: I mixed up the 2 rates
Let A= the final amount, P= initial amount, i= annual simple interest rate, x= annual compound interest rate, n= time (in years)
The formula for compound interest rate is [imath]A=P(1+x)^n=P(1+x)^4[/imath]
The formula for simple interest rate is [imath]A=P(1+i\cdot n)=P(1+0.05\cdot 4)[/imath]
Now equate the 2 equations and solve for [imath]x[/imath]:
[math]P(1+x)^4=P(1+0.05\cdot 4)[/math]
Click to expand...
in the equation why did you put i' on the right side? on the right side is the formula to calculate the simple interest rate, and i'= annual compound interest rate
 
itsrayex said:
in the equation why did you put i' on the right side? on the right side is the formula to calculate the simple interest rate, and i'= annual compound interest rate
Click to expand...
My apologies for the mistake. I've edited my post. Please reread the post. I changed to x so it's consistent with your answer choices.
 
BigBeachBanana said:
My apologies for the mistake. I've edited my post. Please reread the post. I changed to x so it's consistent with your answer choices.
Click to expand...
Np, thank you. Also I tried to follow your suggestion and here's what I got:
1644780628773.png
Which yelds 0.05 and does not match any of the options above. Did I do smth wrong/am I missing something?
 
You wrote (1.05*4)^(1/4) - 1 = 1.431569 -1 = 0.43

You should calculate

(1+0.05*4)^(1/4) - 1 = (1+0.2)^(1/4) - 1 = 1.046635139 - 1 = 0.04664 ......................added
 
Last edited by a moderator:
BigBeachBanana said:
You're missing the order of operation on the right-hand side. Multiplication comes before addition.
Click to expand...
oh you mean at the beginning right? like this:
1644781167071.png
still does not yeld a correct result. I'm sorry, I guess I am messing up somewhere else too
 
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