Question

1. A retirement account is opened with an initial deposit of $8,500 and earns 8.12% interest compounded monthly. What will the account be worth in 20 years? What if the deposit were compounded monthly with simple interest? Could you see the situation in a graph? From what point one is better than the other?

Answer 1

Answer:

Part A) $\ 42,888.48$  

Part B) $A=\ 22,304$

Part C) The graph in the attached figure

Step-by-step explanation:

Part A) What will the account be worth in 20 years?

we know that    

The compound interest formula is equal to  

$A=P(1+\frac{r}{n})^{nt}$  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

$t=20\ years\\ P=\ 8,500\\ r=0.0812\\n=12$  

substitute in the formula above  

$A=8,500(1+\frac{0.0812}{12})^{12*20}$  

$A=8,500(1.0068)^{240}$  

$A=\ 42,888.48$  

Part B) What if the deposit were compounded monthly with simple interest?  

we know that

The simple interest formula is equal to

$A=P(1+rt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

$t=20\ years\\ P=\ 8,500\\r=0.0812$

substitute in the formula above

$A=8,500(1+0.0812*20)$

$A=\ 22,304$

Part C) Could you see the situation in a graph? From what point one is better than the other?

Convert the equations in function notation

$A(t)=8,500(1.0068)^{12t}$ ------> equation A

$A(t)=8,500(1+0.0812t)$  -----> equation B

using a graphing tool  

see the attached figure  

Observing the graph, from the second year approximately the monthly compound interest is better than the simple interest.