If Emery has 1700 to invest at 7 per year compounded monthly

If Emery has $1,700 to invest at 7% per year compounded monthly, how long will it be before he has $2,600? If the compounding is continuous, how long will it be?

Solution

formula for compound interest monthly:

Amount = Principal[ 1+r/12]^(t*12)

2800 = 1700[ 1 +0.07/12]^12t

1.647 = 1.0058^12t

take natural log on both sides:

ln(1.647) = 12*ln(1.0058)

t = 7.149 yrs

Continous Compounding :

Amount = Principal(e^rt)

2800 = 1700 e^(0.07t)

ln(28/17) = 0.07t

t = 7.128 years

Option C