Question

Trey Gorman invests $5,000 in a 1-year certificate of deposit that earns interest at an annual rate of 4% compounded monthly. The amount per $1.00 is 1.040742. How much interest will he earn at the end of one year?

Answer 1

The future value of his investment is $5,203.71. He would have earned an interest of $203.71 by the end of the year.

Answer 2

The interest would be $ 203.707715

Explanation:

Since, the amount after compounded monthly is,

`A=P(1+(r)/(12))^(12t)`

Where, P is the principal amount,

r is the annual rate of interest,

t is time ( in years ),

Here, P = $ 5000,

r = 4 % = 0.04,

t = 1 year,

So, the amount after 1 year would be,

`A=5000(1+(0.04)/(12))^(12* 1)`

`=5000((12+0.04)/(12))^(12)`

`=5000((12.04)/(12))^(12)`

`=5203.707715`

Hence, the interest would be,

`I=A-P`

`=5203.707715-5000`

`=\$ 203.707715`