# Math Help - investment fund question

1. ## investment fund question

A person pays $2000 into an investment fund every six months, and it earns interest at a rate of 6% pa, compounded monthly. How much is the fund worth at the end of ten years? Answer:$55 586.38

2. Originally Posted by ipokeyou
A person pays $2000 into an investment fund every six months, and it earns interest at a rate of 6% pa, compounded monthly. How much is the fund worth at the end of ten years? Answer:$55 586.38
Use the formula

$A = P(1 + r)^n$.

If the rate is $6\%$ per year, then every month the rate is $\frac{6}{12}\% = 0.5\%$.

If it is being compounded monthly for $10$ years, then there are $120$ time periods.

3. If i use the formula i would get $3638.79 which is not correct as the answer is$55 586.38

Because i don't think that formula includes the fact that $2000 is deposited every six months for 10 years. 4. Originally Posted by ipokeyou A person pays$2000 into an investment fund every six months, and it earns interest at a rate of 6% pa, compounded monthly. How much is the fund worth at the end of ten years?
Answer: $55 586.38$55,586.38 is correct IF the 1st deposit is made at BEGINNING.

The rate to be used is the semiannual rate equivalent to 6% cpd monthly,
which is determined this way:
(1 + r)^2 = 1.005^12 ; solve for r

5. Originally Posted by Wilmer
\$55,586.38 is correct IF the 1st deposit is made at BEGINNING.

The rate to be used is the semiannual rate equivalent to 6% cpd monthly,
which is determined this way:
(1 + r)^2 = 1.005^12 ; solve for r
Could you show me how you got that? I don't understand where you got the LHS of the equation. And is 12 meant to be 120? I can't solve for r.

6. (1 + r)^2 = 1.005^12 ; solve for r
Originally Posted by ipokeyou
Could you show me how you got that? I don't understand where you got the LHS of the equation. And is 12 meant to be 120? I can't solve for r.
LHS represents a rate r compounded semiannually, hence to power 2.

12 is meant to be 12; 12 months in a year.

(1 + r)^2 = 1.005^12
r = SQRT(1.005^12) - 1

7. Originally Posted by Wilmer
(1 + r)^2 = 1.005^12 ; solve for r

LHS represents a rate r compounded semiannually, hence to power 2.

12 is meant to be 12; 12 months in a year.

(1 + r)^2 = 1.005^12
r = SQRT(1.005^12) - 1
Oh I see. So I got r = 0.03037... and if I were to sub it into the formula A = P(1 + r)^n , with n = 120 and p = 2000 I will get 72542.82. Is this what you mean? I'm still close to the answer but not there yet. Did I use the wrong formula?

8. Originally Posted by ipokeyou
Oh I see. So I got r = 0.03037... and if I were to sub it into the formula A = P(1 + r)^n , with n = 120 and p = 2000 I will get 72542.82. Is this what you mean? I'm still close to the answer but not there yet. Did I use the wrong formula?
That's NOT the correct formula; here:
Future value of an annuity - Google Search=

And n = 20, NOT 120

r = .03037... is correct

9. Originally Posted by Wilmer
That's NOT the correct formula; here:
Future value of an annuity - Google Search=

And n = 20, NOT 120

r = .03037... is correct
Problem solved! Thank you very much!