By a condition of a will, the sum of Php 2.5M is left to a son to be held in a trust fund by his guardian until it amounts to Php 4.5M. When will th son receive the money if the fund is invested at 12% compounded quarterly.
2.5(1 + .12/4)^(4x) = 4.5
1.03^(4x) = 1.8
4x ln1.03 = ln1.8
x = ln1.8/(4ln1.03) = 4.97 years
5 YEARS
To calculate when the son will receive the money, we need to determine how long it will take for the trust fund to grow from Php 2.5M to Php 4.5M at an interest rate of 12% compounded quarterly.
To solve this, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (Php 4.5M)
P = Principal amount (Php 2.5M)
r = Annual interest rate (12% or 0.12)
n = Number of times interest is compounded per year (quarterly, so 4)
t = Number of years
Plugging in the given values, we can rearrange the formula to solve for t:
4.5M = 2.5M(1 + 0.12/4)^(4t)
Dividing both sides by 2.5M:
1.8 = (1.03)^(4t)
Taking the logarithm of both sides (base 10 or natural logarithm, it doesn't matter):
log(1.8) = log[(1.03)^(4t)]
Using the properties of logarithms (log(a^b) = b * log(a)):
log(1.8) = 4t * log(1.03)
Dividing both sides by 4 * log(1.03):
t = [log(1.8)] / [4 * log(1.03)]
Using a calculator, we can compute the value of t:
t ≈ 7.84 years
Therefore, it will take approximately 7.84 years for the trust fund to grow from Php 2.5M to Php 4.5M, compounded quarterly at an interest rate of 12%. The son will receive the money after around 7.84 years.