Question

Marco invested $3000 into a fund that is expected to grow by 4.23% per year. How long will it take the fund to be worth $6000?​

Answer 1

Answer:

$6000 = 3000(1+0.0424)^{t}$

t = 16.73 years

Step-by-step explanation:

This can be solved using the "exponential growth" formula.

Steps:

A = Final Amount

S = Starting Value

r = rate

c = times in a year ( c = 1 in this equation which is why it's not shown in the actual equation )

1. $A=S(1+\frac{r}{c})^{ct}$ → cancel out S →  $\frac{A}{S} = \frac{S(1+\frac{r}{c})^{ct} }{S}$

2. $\frac{A}{S} = {(1+\frac{r}{c})^{ct} }$  → sperate ct from equation by logging both sides (logging a value with an exponent brings the exponent in front of log)  → $log(\frac{A}{S}) = ctlog(1+\frac{r}{c})$

3. $log(\frac{A}{S}) = ctlog(1+\frac{r}{c})$ → transfer right side log to left side along with the c value to only have t remaining → $\frac{log(\frac{A}{S})}{clog(1+\frac{r}{c})} = \frac{ctlog(1+\frac{r}{c})}{clog(1+\frac{r}{c})}$

4. Solve for answer: $\frac{log(\frac{A}{S})}{clog(1+\frac{r}{c})} = t$