# The formula for calculating the amount of money returned for deposit money into a bank account or CD?

Suppose you deposit \$20,000 for 3 years at a rate of 8%. If a bank compounds continuous, then the formula becomes simpler, that is

where e is a constant and equals approximately 2.7183. Now suppose, instead of knowing t, we know that the bank returned to us \$25,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t).

Relevance

ok it sounds like you know how to do this, but just dont want to number crunch... anyway i'll start from the top.

let's set up a formula that relates current value, future value, interest rate and time.

25,000 = 20,000(1.08)^t

first thing to do is get rid of that 20,000... so it becomes

1.25 = 1.08^t

take the log of each side and bring the t down.

log1.25 = t log1.08

so t = log1.25/log1.08

t = 2.899435195 years

• ?
Lv 4
4 years ago

The formulation for the uniform sequence (A) back given a modern-day properly worth (P) is: A = P[(i(one million+i)^n]/[(one million+i)^n-one million] the place i is the useful interest cost, i =[one million+r/m]^m the place r is the nominal (annual) interest cost and m is the form of compounding sessions. n is the form of years. Sorry for changing extremely some the notation, yet it extremely is the way I found out it.

formula for calculating the amount receivable when the amount is compounded annually....

amount= p(1 + r/100)^t

where p= principal

r=rate of interest

t=period for which the principal is left in a/c

taking values of different variables

25000=20000(1.08)^t

=>1.25=(1.08)^t

taking log on both sides,

log(1.25)=t log(1.08)

=>0.09691=t(0.03342)

=>t=2.9 yrs