To solve this problem, we will use the formula for compound interest, which is:

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

Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money)
r = annual interest rate (in decimal)
n = number of times that interest is compounded per year
t = the time the money is invested for in years

In this case, we know that:
A = Php2,385.63
P = Php2,000
r = 6% or 0.06 (in decimal)
n = 2 (since it is compounded semi-annually)

We need to find t.

So, we can rearrange the formula to solve for t:

t = ln(A/P) / (n * ln(1 + r/n))

Substituting the given values:

t = ln(2385.63/2000) / (2 * ln(1 + 0.06/2))

Now, calculate the values:

t = ln(1.192815) / (2 * ln(1.03))

t = 0.1785 / 0.029558

t = 6.03 years

So, it took approximately 6 years for the investment to grow to Php2,385.63.

Question

To solve this problem, we will use the formula for compound interest, which is:

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

Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money)
r = annual interest rate (in decimal)
n = number of times that interest is compounded per year
t = the time the money is invested for in years

In this case, we know that:
A = Php2,385.63
P = Php2,000
r = 6% or 0.06 (in decimal)
n = 2 (since it is compounded semi-annually)

We need to find t.

So, we can rearrange the formula to solve for t:

t = ln(A/P) / (n * ln(1 + r/n))

Substituting the given values:

t = ln(2385.63/2000) / (2 * ln(1 + 0.06/2))

Now, calculate the values:

t = ln(1.192815) / (2 * ln(1.03))

t = 0.1785 / 0.029558

t = 6.03 years

So, it took approximately 6 years for the investment to grow to Php2,385.63.

Knowee AI · Accepted Answer