Question

After 6 years, what is the total amount of a compound interest investment of $35,000 at 4% interest, compounded quarterly? $37,153.21 $39,438.88 $44,440.71 $56,295.30

Answer 1

The given rate of interest is 4% compounded quarterly. This is a nominal rate of interest. To make it an effective rate of interest,

$i_{eff}$ = $(1 + \frac{i}{m} )^{m} -1$, where m is the number of periods in a year. There are 4 quarters in a year, so m =4. So,

$i_{eff}$  = $(1 + \frac{0.04}{4} )^{4} -1$= 0.0406

The working equation is

$F = P (1 + i_{eff})^{n}$, where n=6, P = $35000,

$F = 35000 (1 + 0.0406))^{6}$

F = $44,440.71

Answer 2

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  

$t=6\ years\\ P=\ 35,000\\ r=0.04\\n=4$  

substitute in the formula above  

$A=35,000(1+\frac{0.04}{4})^{4*6}$  

$A=35,000(1.01)^{24}$  

$A=\ 44,440.71$  

therefore

the answer is the option

$\ 44,440.71$