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If you were to place $2,500 in a savings account that pays 5% interest compounded continuously, how much money will you have after 10 years? Assume you make no other deposits or withdrawals.

How would I go about finding this?

Verified Answer :

syed514

But using the formula makes this much simpler, P(1+r/n)^nt
F = Future value

P = present value

r = annual interest rate written as a decimal

t = number of years

F = 2500(2.71)^0.5
   = 4121.8

InesWalston

Answer-

You will get $4121.80 after 10 years.

Solution-

You added $2,500 in a savings account with a 5% interest compounded continuously for 10 years.

The formula for continuous compounding is,

\(A=Pe^{r\cdot t}\)

Where,

A = Future amount

P = Principal = $2500

r = Rate of interest = 5% = 0.05

t = Time period = 10 years

Putting the values,

\(A=2500e^{0.05\times 10}\)

\(=2500e^{0.5}\\\\=\$4121.80\)