Question

Holly wants to save money for an emergency. Holly invests $500 in an account that pays an interest rate of 6.75% How many years will it take for the account to

reach $14,300? Round your answer to the
nearest hundredth.

Answer 1

51.339

Explanation:

Hello,

At the beginning Holly has $500

After one year

he will get 500*(1+6.75%)=500*1.0675

After n year (n being real)

he will get

`500\cdot1.0675^n`

and we are looking for n so that

`500\cdot1.0675^n=14,300\\<=> ln (500\cdot1.0675^n)=ln(14,300)\\<=>ln(500)+n\cdot ln(1.0675)=ln(14,300)\\<=> n= (ln(14,300)-ln(500))/(ln(1.0675))=51.338550...\\`

so we need 51.339 years

Hope this helps