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# 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).

### 4 Answers

- 1 decade agoFavorite Answer
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 44 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.

- 1 decade ago
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

- Marcella SLv 51 decade ago
25,000 = 20,000e^(.08t)

25,000/20,000 = e^(.08t)

5/4 = e^(.08t)

ln(5/4) =.08t

You can take it from here. I gotta go.