How much must be deposited today into the following account in order to have $ 65000 in 7 years for a down payment on a house? Assume no additional deposits are made.
An account with annual compounding and an APR of 8%
65000 = a (1 + .08)^7
log(a) = log(65000) - [7 log(1.08)]
Well, if you're looking to save for a house, you might want to consider investing in a clown-shaped piggy bank. It'll keep your money safe and provide some entertainment when you're feeling down about all those bills. As for the amount, let's do some math. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the accumulated amount, P is the principal (initial deposit), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. We're given r = 8%, n = 1, t = 7, and we want to solve for P when A = $65,000. Now, here comes the fun part... crunching numbers! Solving the equation, we get P = $41,379.31. So, if you deposit exactly $41,379.31 into the account today, you'll be one step closer to that house. Good luck, and remember, always keep a red clown nose handy for those stressful moments!
To calculate the amount that must be deposited today, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Future value (desired amount)
P = Principal (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, we know that the desired future value is $65000 and the deposit will be made for 7 years. The annual interest rate is 8% (or 0.08 in decimal form) and the compounding is done annually (n = 1).
Let's plug in the given values into the formula:
65000 = P(1 + 0.08/1)^(1*7)
Now we can solve for P:
65000 = P(1 + 0.08)^7
65000 = P(1.08)^7
65000 = P * 1.717993
P = 65000 / 1.717993
P ≈ $37,855.48
Therefore, in order to have $65000 in 7 years for a down payment on a house, approximately $37,855.48 needs to be deposited today into the account with an APR of 8% and annual compounding.
you use the formula
f= p*(1+(r/n))^nt
where f = future value
p=present value
r = rate
n = number of compounding periods per year
t = number of years
so you do
65000= p (1+0.08/12)^(12*7)
and you solve for p
anonymous used monthly compounding, it said "compounded annually"
so
p = 65000/(1.08)^7 = 37926.87
(same answer that R_scott got with his log method)