lucy invests $800 in an account that earns 6.12% annual interest compounded continuously. juan invests $1600 in an account that earns 3.9% annual interest compounded continuously. find when the value of lucys investment equals the value of juans investment?

Both their investments will reach a similar value in 32 years, 9 months and 8 days. Both accounts will have exactly $5,606.

Explanation:

Original investment: $800 at 6.12% $1,600 at 3.9%

future value 10 years $1,449 $2,346

future value 20 years $2,624 $3,439

future value 30 years $4,753 $5,042

future value 31 years $5,044 $5,238

future value 32 years $5,353 $5,442

future value 33 years $5,681 $5,655

It will take over 32 years for both investments to match their amounts.

to determine the approximate month we start with the future value in 32 years:

$5,353 $5,442

future value in 6 months $5,517 $5,548

future value in 9 months $5,599 $5,601

future value in 9 months

and 5 days $5,603 $5,604

future value in 9 months

and 8 days $5,606 $5,606