Question

john invested $2000 that earn interest at 4% per annum compounded monthly. two year later the interest rate is 4.50% compounded quaterly. determine the accumulated value of investment two year after the change

Answer 1

Answer:

$\ 2,369.11$  

Step-by-step explanation:

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  

Part 1)

$t=2\ years\\ P=\ 2,000\\ r=0.04\\n=12$  

substitute in the formula above

$A=2,000(1+\frac{0.04}{12})^{12*2}$  

$A=2,000(1.0033)^{24}$  

$A=\ 2,166.29$  

Part 2)

$t=2\ years\\ P=\ 2,166.29\\ r=0.045\\n=4$  

substitute in the formula above

$A=2,166.29(1+\frac{0.045}{4})^{4*2}$  

$A=2,166.29(1.01125)^{8}$  

$A=\ 2,369.11$