If an apartment complex will need painting in 3 1/2 years and the job will cost $25,000, what amount needs to be deposited into an account now in order to have the necessary funds? The account pays 8% interest compounded semiannually.
(a) State the type of the problem.
future value
present value
ordinary annuity
amortization
sinking fund (I think it may be this one
(b) Answer the question. (Round to the nearest cent.)
Thank you
The compound interest formula is
A = P * [1 + (r/n)]^(n * t)
P = principal amount (the initial amount you borrow or deposit)
r = annual rate of interest (as a decimal)
t = number of years the amount is deposited or borrowed for.
A = amount of money accumulated after n years, including interest.
n = number of times the interest is compounded per year
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In this case you're trying to find P, the amount that needs to be deposited now.
P = principal amount (the initial amount you borrow or deposit)
r = 0.07
t = 3.5
A = 25,000
n = 2
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Rearranging the equation to solve for P gives
P = { A / [1 + (r/n)]^(n * t) }
It wouldn't let me post it all together so i posted it in two.
This isn't my work I got it from YA! :D
Oh wait the percent is wrong!!
Follow his steps just use your numbers i guess so sorry didn't notice that!
(a) The type of problem in this scenario is a sinking fund problem. A sinking fund is a type of savings account where money is accumulated over time to meet a specific future financial obligation.
(b) To calculate the amount that needs to be deposited into the account now, we need to use the formula for the future value of a sinking fund. The formula is:
FV = PV * (1 + r/n)^(nt)
Where:
FV = Future value (the amount needed for the painting job)
PV = Present value (the amount to be deposited now)
r = Interest rate (8% in this case)
n = Number of times that interest is compounded per year (semiannually, so n = 2)
t = Number of years (3.5 years)
Applying the formula:
25000 = PV * (1 + 0.08/2)^(2*3.5)
To solve for PV, we need to isolate it:
PV = 25000 / (1 + 0.08/2)^(2*3.5)
Calculating this expression will give us the amount that needs to be deposited into the account now in order to have the necessary funds.