A person desires to create a fund to be invested at 10% compound interest per annum to provide for a price of 300 every year. The amount we should invest is:

Answer 1

To determine the amount that needs to be invested, we can use the formula for compound interest:

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

Where:
A = the desired annual payment of 300
P = the principal amount (the amount to be invested)
r = the interest rate per annum (10% or 0.1)
n = the number of times interest is compounded per year (considering it compounds annually, n = 1)
t = the number of years

We want to solve for P, so we rearrange the formula:

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

Plugging in the given values:
A = 300
r = 0.1
n = 1

P = 300 / (1 + 0.1/1)^(1*t)

Since there is no specific time mentioned, we can assume it is invested for an indefinite period. Thus, t goes to infinity.

As t approaches infinity, (1 + 0.1/1)^(1*t) becomes (1 + 0.1)^(1*t) = (1.1)^(1*t) = (1.1)^t.
The investment will only be enough to provide an annual payment of 300 if the interest keeps growing at the same rate.

So, for the amount to be invested, we require P = (A / (1 + r/n)^(nt)) = (300 / (1.1)^t).

Note: Without specifying a certain time period, it is not possible to calculate the exact amount to be invested.