How much money would you have to put into an account initially in order to have $5000 after 15 years if the account pays 6% interest compounded monthly?

Question

 How much money would you have to put into an account initially in order to have $5000 after 15 years if the account pays 6% interest compounded monthly?

Answer 1

The equation for compounded interest is as follow:

P = C (1 + r/n)^nt

where:

P = ending amount

C = beginning amount

r = interest rate (as a decimal)

n = number of times per year the interest is compounded

t = number of years

 

For your example:

P = $5000

C is unknown

r = 0.06

n = 12 times per year

t = 15 years

 

Now Plugging in numbers:

(5000) = C [1 + (.06)/(12)]^(12)(15)

(5000) = C [1.005]⁽¹⁸⁰⁾

(5000) = C (2.454093562)

 

C = (5000) / (2.454093562)

 

C = 2037.412134

This rounded is $2037.41.

This may be the answer but technically this amount would be slightly insufficient to get $5000 after 15 years since it is rounded. To make sure to have the $5000, you would need to round the answer up to $2037.42.

 

I hope this helps!

Answer 2

The formula for compound interest is A = P (1 + r/n) ^ nt

A=total amount  p=initial amount  r=rate  n=# of payments (12 months/year)  t=time (1 year)

5000=p(1+.06/12)^(12*15)

Multiply what is in the parenthesis 

5000=p(1.005)^180

calculate (1.005)^180

5000=p(2.4540936)    aprox.

Divide both sides by by 2.454..... to get

p=$2037.412102    aprox.