Question

Zhong has money to invest in one of two accounts for 2 years.Account 1 requires a $1,200 investment and earns 2.7% interest compounded daily.Account 2 requires a $1,000 investment and earns 3.9% interest compounded annually.Which account has a higher return?Account 2 because it earns $14.41 more than Account 1Account 2 because it earns $12.94 more than Account 1Account 2 because it earns $24.04 more than Account 1Account 2 because it earns $28.85 more than Account 1

Answer 1

The rule of the compounded interest is

$A=P(1+\frac{r}{n})^{nt}$

Where:

A is the new amount

P is the initial amount

r is the rate in decimal

n is a number of periods per year

t is the time in years

For the first account:

P = 1200

r = 2.7% = 2.7/100 = 0.027

n = 365 ------ compounded daily

t = 2

$\begin{gathered} A=1200(1+\frac{0.027}{365})^{365\times2} \\ A=1266.58 \end{gathered}$

The account will have $12665.79 in 2 years

For the second account:

P = 1000

r = 3.9% = 3.9/100 = 0.039

n = 1 ------- compounded annually

t = 2

$\begin{gathered} A=1000(1+\frac{0.039}{1})^{1\times2} \\ A=1079.52 \end{gathered}$

The account will have $1079.52

Let us find the difference between them

$\begin{gathered} d=1266.58-1079.52 \\ d=187.06 \end{gathered}$

The first account is more by $187.06