Question

Nicole opens a savings account with an initial deposit of $5,000. since then, she has never made any other deposits or withdrawals. her savings account earns 4℅ intrest compounded monthly. which equation gives the approximate amount, A(x), she has in her savings account as a function of x, the number of years since her initial deposit?

1. A(x)= 5,000^(0.96x)

2. A(x)= 5,000(0.959)^x

3. A(x)= 5,000 + 0.04x

4. A(x)= 5,000^(1.04x)

5. A(x)= 5,000(1.041)^x​

Answer 1

Option 5.
`A(x)=\$5,000(1.041)^(x)`

Explanation:

we know that

The compound interest formula is equal to

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

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

`t=x\ years\\ P=\$5,000\\ r=0.04\\n=12`

substitute in the formula above

`A=\$5,000(1+(0.04)/(12))^(12x)`

`A=\$5,000(1.041)^(x)`