Question

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A savings account is started with an initial deposit of $600. The account earns 2.1 % interest compounded annually.
(a) Write an equation to represent the amount of money in the account as a function of time in years.


(b) Find the amount of time it takes for the account balance to reach $800. Show your work.

Answer 1

Answer:

Part a) $A=600(1.021)^{t}$  

Part b) $t=13.84\ years$

Step-by-step explanation:

Part a)

we know that    

The compound interest formula is equal to  

$A=P(1+\frac{r}{n})^{nt}$  

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  

$P=\ 600\\ r=2.1\%=2.1/100=0.021\\n=1$  

substitute in the formula above

$A=600(1+\frac{0.021}{1})^{1*t}$  

$A=600(1.021)^{t}$  

Part b) For $A=\ 800$

substitute in the expression

$A=600(1.021)^{t}$  

$800=600(1.021)^{t}$  

simplify

$\frac{8}{6}=(1.021)^{t}$  

Apply log both sides

$log(\frac{8}{6})=log[(1.021)^{t}]$

$log(\frac{8}{6})=(t)log(1.021)$

$t=log(\frac{8}{6})/log(1.021)$

$t=13.84\ years$