Question

How much more would $8,000 earn in four years compounded daily at 5% than compounded annually at 5%?

Answer 1

Given the statement:

8,000 earn in four years compounded daily at 5%

To find the amount we use formula:

`A = P(1+(r)/(n))^(nt)`

where P is the principal , A is the amount , n is number of times compounded per year and t is the time in year.

Here, Principal(P) = $8000, r = 5% and n = 365

Substitute these given values we get;

`A_1= 8000(1+(5)/(365))^(365 \cdot 4)`

`A_1= 8000 \cdot 1.000137^(1460)`

`A_1= 8000 \cdot 1.22141`

Simplify:

`A_1= \$9771.28`

To find the Interest we use formula:

`I_1= A_1-P`

`I_1= 9771.28 -8000 = \$1771.28`

It is also given that:

8,000 earn in four years compounded annually at 5%.

Here, P = $8000, r = 5% , t =4 year and n = 1

Using the same formula to calculate the amount:

`A_2 = 8000(1+(5)/(1))^(1 \cdot 4)`

`A_2= 8000(1.05)^4`

Simplify:

`A_2= \$9724.05`

To find the Interest :

`I_2= A_2 - P`

`I_2= 9724.05 - 8000= \$1724.05`

Then;

`I_1-I_2 = 1771.28-1724.05 = \$47.23`

Therefore, $47.23 more would $8,000 earn in four years compounded daily at 5% than compounded annually at 5%