Question

You want to have $28,000 saved 3 years from today in order to make a down payment on a house. To fund this, you will make deposits each week from your paycheck into an account that will earn 5.18 percent compounded weekly. How much must you deposit each week

Answer 1

$167.26must be deposited each week

Step-by-step explanation:

Given FV = $28000, n = 3 years, r = 5.8% pmt =?

Use the FV of annuity formula

FV = pmt *[(1+r)^n - 1/r]

We looking for weekly payments made for a period of 3 years

there are 52 weeks in a year

n = 53*3 = 156

r = 5.18/52 =0.0009

Substitutte in the formula

28000= pmt *[(1.0009)^156-1/0.0009]

28000 = pmt (167.40)

pmt = 28000/167.40=$167.26

Answer 2

= $165.991

Step-by-step explanation:

The deposit each week can be determined using the the sinking fund formula.

A sinking fund is an investment plan where a fixed amount of money is deposited into an interest-yielding account to accumulate a target sum in the future.

Equal deposit = FV/ annuity factor

Annuity factor =((1+r)^(n) - 1)/r

FV = future amount, - $28,000

r - interest rate per period - 5.18%/52 = 0.0996% per week. Remember that there are 52 weeks in a year

n - number of period = 3× 52 = 156 weeks

Annuity factor =( (1 +0.099%)^(156)-1)/0.0996%

= 168.6835499

Deposit per week

= 28,000/ 168.683

= $165.991

FV = A × ((1+r)^(n) - 1)/r