can someone check my work

Question

So the question is

How much money needs to be invested now to obtain $5000 in 10 years if the interest rate in a CD is 2.25%, Compounded monthly. To round the the nearest cent.

 

 

So I Used p=a/(1+rt)

P=5000/(1+(0.0225x10)) = 4081.63265

P=$4081.63

 

so when i plug it into a=p(1+rt)

A=4081.63(1+0.0225x10)=4999.996

A=$ 5000

 

did i do that right.

Answer 1

Lindsay,

 

It appears 2.25% is the annual interest compounded monthly.

 

The correct formula would be

 

P = A/[(1+r/n)^(nt)], where n is the frequency of compounding, 12 in this case

r/n = .0225/12 = .001875

t = 10 years

nt = 120

 

P = 5000/(1.001875)¹²⁰

P = 5000/1.252

P = $3,993.42