Use graphical approximation techniques or an equation solver to approximate the desired interest rate. A person makes annual payments of $1000 into an ordinary annuity. At the end of 5 years, the amount in the annuity is 5767.98. What annual nominal compounding rate has this annuity earned?

Rate needs to be rounded 2 decimal places.

Question

Use graphical approximation techniques or an equation solver to approximate the desired interest rate. A person makes annual payments of $1000 into an ordinary annuity. At the end of 5 years, the amount in the annuity is 5767.98. What annual nominal compounding rate has this annuity earned?

Rate needs to be rounded 2 decimal places.

anonymous · Answer

$$x^5 = 767.98$$

amistre64 · Answer

the present value of an annuity should be 0; also refered to as an internal rate of return i think

amistre64 · Answer

1000/(1+r)^1
1000/(1+r)^2
1000/(1+r)^3
1000/(1+r)^4
1000/(1+r)^5
-------------
sum = 5767.98

amistre64 · Answer

lol, almost had that right ....

amistre64 · Answer

sum would have to be zero for net present value :)

best thing to do according to my accounting classes was to guess at it

amistre64 · Answer

$$FV=PV\frac{1-(1+r)^n}{r}$$
$$5767.98=1000\frac{1-(1+r)^5}{r}$$
$$5.76798=\frac{1-(1+r)^5}{r}$$
$$5.76798r=1-(1+r)^5$$
see where the 2 graphs intersect

amistre64 · Answer

forgot a negative but i get about 7.15% http://www.wolframalpha.com/input/?i=y%3D-5.76798x%2C+y%3D1%E2%88%92%281%2Bx%29%5E5 http://www.wolframalpha.com/input/?i=-1000%281-%281.0715%29%5E5%29%2F%28.0715%29