math please help me

Question

You deposit $5000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 20 years?

Answer 1

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

Given the information provided, P=5000, r=.07 (Change 7% to a decimal), n=1 (annually), t=20 (time in years)

So you are trying to solve for A to determine how much money is in the account after 20 years.

A=5000(1+.07/1)^1*20

A=5000(1.07)^20

A=5000(3.86968446)

A=19348.422

If you think about like they are taking $5000 and multiplying by 1.07 (adding 7%) each year, this answer makes sense.

At the end of year 1 there is 5350. Year 2 would be 5350*1.07=5724.50, year 3 ends with 6125.22. If you continued multiplying the previous answer by 1.07, you should end up with $19,348.42.

Answer 2

You're paying $5,000/yr into an account earning 7% interest compounded annually. What is the balance after 20 years? Think of it as a series of $5,000 deposits, the first of which earns interest for 20 years, the 2nd for 19 years, etc.

The formula is A = PMT x [(1 + APR/n)^(nY) - 1]/(APR/n) where A = accumulated balance, PMT is regular deposit amount, APR is annual percentage rate (decimal), n = no. of payment periods/yr, Y = no. of years.

A = 5000 x [1 + 0.07/1)^1x20 - 1]/(0.07/1) ≅ $204,977

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