By the conditions of a will, the sum of P25,000 is left to a girl to be held in trust by her guardian until it amounts to 45,000. when will the girl receive the money if the fund is invested at 8% compounded quarterly?? please show the solution.. thank you:)

8%/4 = 2% per quarter

so every three months multiply by 1.02

25 * 1.02^n = 45

1.02^n = 1.8

n log 1.02 = log 1.8

n = 29.68 quarters
or 7.42 years

F=P*(1+i)^n --->formula

1.02 is from (1+.02)
since 8% compounded Quarterly..
8%/4=0.02

wooow..thanks:)

how you get 1.02

7.42 thank you very much.

To find out when the girl will receive the money, we need to calculate the time it takes for the initial amount of P25,000 to grow to P45,000 when invested at 8% compounded quarterly.

The formula to calculate the future value of an investment with compound interest is:

FV = PV * (1 + r/n)^(n*t)

Where:
FV = Future Value
PV = Present Value (initial amount)
r = annual interest rate in decimal form
n = number of times interest is compounded per year
t = time in years

In this case, PV is P25,000, r is 8% (which equals 0.08 in decimal form), and n is 4 (quarterly compounding). We need to find out the time t.

Let's rearrange the formula to solve for t:

FV = PV * (1 + r/n)^(n*t)
Divide both sides by PV:
FV / PV = (1 + r/n)^(n*t)
Take the natural logarithm of both sides:
ln(FV / PV) = ln((1 + r/n)^(n*t))
Apply the exponent rule:
ln(FV / PV) = n*t * ln(1 + r/n)
Divide both sides by (n * ln(1 + r/n)):
ln(FV / PV) / (n * ln(1 + r/n)) = t

Now we can substitute the values into the formula and solve for t:

FV = P45,000
PV = P25,000
r = 8% = 0.08
n = 4

Plugging in these values, the formula becomes:

ln(45,000 / 25,000) / (4 * ln(1 + 0.08/4))

Using a calculator, evaluate the right-hand side of the equation to find:

t ≈ 3.39

Therefore, it will take approximately 3.39 years for the initial amount of P25,000 to grow to P45,000 when invested at 8% compounded quarterly. The girl will receive the money after 3.39 years.