Question

1. Suppose you have 16 tubes of paint. How many distinct color groupings can you make with your paint?

2. You deposit $3000 each year into an account earning 6% interest compounded annually. How much will you have in the account in 20 years?

3. Suppose you want to have $300,000 for retirement in 25 years. Your account earns 4% interest. How much would you need to deposit in the account each month?

Answer 1

Question 1:

Total tubes of paint = n = 16

Distint colors available = 16

Distint color groupings can make with paint = 2n

= 216

= 65,536

Therefore, distinct color groupings can make with paint is 65,536

Question 2:

Annual Deposit = P = $3,000

n = 20 years

r = interest rate = 6%

Future value of annuity = P[(1+r)^n - 1] / r

= $3,000 [(1+6%)^20 - 1] / 6%

= $3,000 * 2.20713547 / 0.06

= $110,356.774

Therefore, Account balance in 20 years is $110,356.77

Question 3:

Let Monthly Deposit = P

n = 25*12  = 300 months

r = interest rate = 4%/12 = 0.333333%

Future value of annuity = P[(1+r)^n - 1] / r

$300,000 = P[(1+0.333333%)^300 - 1] / 0.333333%

$1,000 = P* 1.71376245

P = $583.511

Therefore, Monthly deposit to have $300,0000 in 25 years is $583.51