Question

An investment of $250,000 which earn interest at the rate of 10% per year is made. If the interest is compounded continuously, compute the amount to which the investment will grow after 20 years

Answer 1

Answer:

it will take 4 years.

Explanation:

The formula for this account is

FV = 250000*(1+(0.12/4))*n,

where FV is the future value and "n" is the number of quarters.

So, you should solve this equation to find n

400000 = 250000*0.13^n.

First, divide both sides by 250000. You get

400000/250000 = 1.03^n, or

1.6 = 1.03^n.

Next, take logarithm base 10 of both sides

log(1.6) = n*log(1.03).

Hence, n = log(1.6)/log(0.3) = 15.90 (rounded).

You want to find the number of quarters, which is an integer number.

Therefore, you round the value of 15.90 to the nearest greater integer, where next compounding will happen.

In this way, you get your

ANSWER. 16 quarters, or 4 years