Solve for Z5

[FinanceNewbie]

I started a course in finance and one of the questions was the following. I tried solving it. Could you please let me know if it's correct?
Solve for Z5
$1,000 = $681.20(1+Z5/2)¹⁰

Solution: (according to me)
(1+Z5/2)¹⁰ = $1,000/$681.20

(1+Z5/2) = ¹⁰√($1,000/$681.20)

Z5/2 = ( ¹⁰√($1,000/$681.20) ) - 1

Z5 = [ ( 1.0391 - 1 ) ] × 2

Z5 = 0.078 (3 d.p)

 

[Cubist]

Well done, it is correct! You can quickly check this for yourself by putting the value of Z5 back into the RHS of your original equation.

You can also use this method to explore the effect that rounding to different dp has, since you might want the answer to be accurate to the nearest cent:-

681.2*(1+ 0.078 /2)^10 = 998.69
681.2*(1+ 0.0783 /2)^10 = 1000.13
681.2*(1+ 0.07827 /2)^10 = 999.99
681.2*(1+ 0.078273 /2)^10 = 1000.00

 

[FinanceNewbie]

Thank you Sir.

Just out of curiosity, what is this type equation called? I wanted to find a few more examples to practice but I don't know how to identify them.

 

[Cubist]

Try searching for "Compound interest", "compound interest questions", "compound interest examples" etc