Question

Nicole opened 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% interest 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?

Answer 1

`A(x)=\$5,000(1.04)^(x)`

Explanation:

we know that

The compound interest formula is equal to

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

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

x is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

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

substitute in the formula above

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

`A(x)=\$5,000((12.04)/(12))^(12x)`

`A(x)=\$5,000(1.04)^(x)`