I would like to have $600000 in 30 years. If I make equal monthly payments in this account that earns 8% interest compounded monthly.

Question

I would like to have $600000 in 30 years. If I make equal monthly payments in this account that earns 8% interest compounded monthly. How much should these monthly deposits be?

Answer 1

30 years is 360 months.

This is going to be a problem involving the sum of a geometric series....and I don't have a calculator right now, so I can't finish the problem for you.... but it goes like this.

 

The first payment, P, is going to be compounded 359 times at 1.00666666....so month 1 is P(1.0066666)³⁵⁹.

The next payment will be compounded 358 times at the same rate...............so month 2 is P(1.0066666)³⁵⁸.

The next month will be P(1.0066666)³⁵⁷ and so on until the last month which will be compounded one time

so P(1.066666).

 

This sum must add to 600,000.n If you factor out the P from each months expression in the sum, you'd get

 

P(1.00666³⁵⁹+1.00666³⁵⁸+1.00666³⁵⁷+......+1.00666²+1.00666+1) = 600,000

 

The sum formula for a geometric series is (1-rⁿ)/(1-r). So 600,000/ your answer is how much each monthly payment should be.

 

Hope this helped

Answer 2

Use the compound interest formula

 

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

 

where:

A = money accumulated

P = investment

r = interest rate

t = time in years

n = number of time compounded per year

 

 

Given:

A = 600000

r = 0.08

t = 30

n = 12

 

 

Let's solve for P first. Divide both sides of equation by (1 + (r / n))^nt.

 

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

 

Now plug in the given values.