By what percentage has it grown after all 35 years? (3 decimal accuracy)

Question

an investment in a long term fund grows by 2% for 25 years, then it grows by 3.5% for 10 years. By what percentage has it grown after all 35 years? (3 decimal accuracy)

 

 

Explanation as well. Don't understand at all how to set it up. 

Answer 1

Hi Joe,

 

Let P be your principal investment.  I''m just using P as a placeholder -- we'll never care how much money it is.

 

After the first year, your investment has grown by 2%, and you now have 

 

P + P*0.02

 

= P*(1.02) 

 

in the bank.

 

After the second year, your investment has grown by another two percent, so your P*(1.02) has grown to

 

P*(1.02) * 1.02

 

= P * 1.02²

 

After the third year, your P * 1.02² has grown yet another 2 percent, and you now have

 

P*1.02² * 1.02

 

= P*1.02³

 

After the 25th year, you have

 

P*1.02²⁵

 

But in first year after that, you earn 3.5 percent.  So your P*1.02²⁵ grows to

 

P*1.02²⁵ * 1.035

 

The second year, you earn another 3.5 percent on top of your P*1.02²⁵ * 1.035, and now you have

 

P*1.02²⁵ * 1.035 * 1.035

 

= P*1.02²⁵ * 1.035²

 

Eventually, after the tenth year, your original amount has grown to 

 

P*1.02²⁵ * 1.035¹⁰

 

Now, to get the percentage growth, you have to subtract off what you started with (1 copy of P) and multiply what's left by 100.

 

I'll leave you to come up with that number, shall I?

 

I hope that helps,

Mike