Question

you want to save $12,000 for a downpayment on a house. how much should be put into an account that pays 3.95% interest compounded continuously for 5 years

Answer 1

The formula for continuous compounding is given by:

A = Pe^(rt)

where:

A = final amount

P = principal amount (initial investment)

e = 2.71828 (constant)

r = annual interest rate (as a decimal)

t = time in years

We can solve for P as follows:

P = A/e^(rt)

We know that we want to save $12,000, the interest rate is 3.95%, and the time is 5 years. Substituting these values into the formula, we get:

P = 12000/e^(0.0395*5)

P = 12000/e^0.1975

P = 12000/1.2183

P = 9854.16

Therefore, Max should put $9,854.16 into the account that pays 3.95% interest compounded continuously for 5 years.