212k views
1 vote
How much more would $8,000 earn in four years compounded daily at 5% than compounded annually at 5%?

1 Answer

5 votes

Answer:

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%





User Paranoidhominid
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories