Question

Romolo has $8,000 to invest in one of two accounts for 5 years.Account 1 earns 5% interest compounded quarterly.Account 2 earns 4.5% interest compounded monthly.Which account has a higher return?Account 1 because it earns $241.93 more than Account 2Account 1 because it earns $899.18 more than Account 2Account 2 because it earns $2,781.39 more than Account 1Account 2 because it earns $2,014.37 more than Account 1

Answer 1

Account 1 because it earns $241.93 more than Account 2

Step-by-step explanation:

Here, we want to get the account that will give the higher return value

To get this, we need to get the return value in which each of the accounts will have

Let us look at scenario 1

$8,000 will be invested for 5 years, with an interest rate of 5% quarterly

The formula to use is as follows:

`A\text{ = P(1 + }(r)/(n))^(nt)`

A is the amount after 5 years which we want to calculate

P is the amount invested which is $8000

r is the interest rate which is 5% = 5/100 = 0.05

n is the number of times interest is compounded per year which is 4 (there are 4 quarters in a year)

t is the number of years which is 5

We substitute these vaues into the equation as follows:

`\begin{gathered} A\text{ = 8000(1 + }(0.05)/(4))^(5*4) \\ \\ A\text{ = \$10,256.30} \end{gathered}`

Let us look at scenario 2

We use the same compounding formula but what will be different will be the values

A is the amount after 5 years which we want to calculate

P is the amount invested which is $8000

r is the interest rate which is 4.5% = 4.5/100 = 0.045

n is the number of times interest is compounded per year which is 12(there are 12 months in a year)

t is the number of years which is 5

We substitute these values as follows:

`\begin{gathered} A\text{ = 8000(1 + }(0.045)/(12))^(12*5) \\ \\ A\text{ = \$10,014.40} \end{gathered}`

As we can see, what will be earned in Account 1 will be greater than what will be earned in Account 2

Now, let us calculate the difference as follows:

`10,256.30\text{ -10,014.40 = \$241.90}`