How much would you need to deposit into an account that pays 6.5% interest compounded semiannually to have $10000 after 7 years

Question

Round it to the nearest $100

find this out by using 

A=P(1+r/n)^nt

Answer 1

Good attempt! Actually, you have a few things off.  First, The equation should be PV(Present Value) = FV(Future Value) times PVF_n,i(Present Value Factor, which is the interest rate to the power of the  number of periods) or

PV = FV(1/1+i^{^n}).

 

So the formula should look like this:

 

PV = $10,000(1/1+6.5%^{^2x7})   Note: It is 7 years semiannually, which means 2 interest payments each year.

PV = $10,000(1/1.065^{^14})

PV = $10,000(1/2.414874185)

PV = $10,000(0.414100249)

PV = $4,141

 

I have verified this on an financial accounting calculator and with my intermediate financial accounting textbook, so I know this is correct.

 

Tadeeb the formula is incorrectly set up in your version.  It is $10,000/(1+6.5%)^{^2x7} not $10,000/(1.65/2)^2x7.  I have verified my answer with a financial calculator and the answer is $4,141.

Answer 2

This is a problem in which you will have to work backwards. You have the final amount (A = $10,000), you have the time it takes to make that amount (t = 7), you have the number of times per year that the interest is compounded (n = 1; because annual is once a year), and last but not least you know your interest rate (r = 6.5%).

Plugging into the equation gives you:

$10,000 = P (1 + .065/1)^(1 x 7)

$10,000 = P (1.065)^7

$10,000/(1.065)^7 = P

$6,435.06 = P

That is the amount you would need to deposit!