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: its option D) 17 years

Step-by-step explanation: the answer is 16.7 but you round it up because thats not an option

Answer 2

`6000 = 3000(1+0.0424)^(t)`

t = 16.73 years

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+(r)/(c))^(ct)` → cancel out S →
`(A)/(S) = (S(1+(r)/(c))^(ct) )/(S)`

2.
`(A)/(S) = {(1+(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((A)/(S)) = ctlog(1+(r)/(c))`

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

4. Solve for answer:
`(log((A)/(S)))/(clog(1+(r)/(c))) = t`