Thread: 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

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

.

If the rate is per year, then every month the rate is .

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

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.

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

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.

(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

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?

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

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!