Business College

A deposit of $10,000 is made a year from now, a second deposit of $10,000 is made at the end of the year 5, and a deposit of $3000 is made at the end of year 8. The account earns 6% interest. You want to withdraw an equal amount, X at the end of each year for the next 10 years. What is the amount of X if the goal is to empty the account

Answers

Answer 1

Answer:

$4068.77

Explanation:

We calculate the Future value of all the three deposits at the end of year 8

FV = CF1 *(1+r)^8-1 + CF5*(1+r)^8-5 + CF8 * (1+r)^8-8

FV = 10000 *(1+0.06)^7 + 10000*(1+0.06)^3 + 3000 * (1+0.06)^0

FV = 15,036.30 + 11,910.16 + 3,000

FV= $29,946.46

We have to calculate the annuity payments that have a Present value = $29,946.46

PV = PMT * 1-(1+r)^-n / r

PV = 29,946.46, PMT= ?, r = 6%, n = 10

29,946.46 = PMT * 1-(1+0.06)^-10 / 0.06

29,946.46 = PMT * 1 - 1.06^-10 / 0.06

29,946.46 = PMT * 1 - 0.558395 / 0.06

29,946.46 = PMT * 0.441605 / 0.06

29,946.46 = PMT * 7.36008

PMT = 29,946.46/7.36008

PMT = 4068.768274257889

PMT = $4068.77

Thus, amount of X is $4068.77 if the goal is to empty the account.

Related Questions

CAM charges for retail leases in a shopping mall must be calculated. The retail mall consists of a total area of 2.8 million square feet, of which 800,000 square feet has been leased to anchor tenants that have agreed to pay $2 per rentable square foot in CAM charges. In-line tenants occupy 1.3 million square feet, and the remainder is a common area, which the landlord believeswill require $8 per square foot to maintain and operate each year. If the owner is to cover total CAM charges, how much will in-line tenants have to pay per square foot?

Answers

Answer:

$3.08 per square foot

Explanation:

Calculation for how much will in-line tenants have to pay per square foot

First step is to find the common area

Common area = 2,800,000−800,000−1,300,000 Common area= 700,000

Second step is to find Common area operating costs

Common area operating costs = 700,000×8

Common area operating costs= $5.6 million

Third step is to find the Operating costs charged to in-line tenants

Operating costs charged to in-line tenants = 5,600,000−800,000×2

Operating costs charged to in-line tenants = 4,000,000

Last step is to calculate the In-line CAM charges using this formula

In-line CAM charges=Operating costs charged to in-line tenants -In-line tenants square feet

Let plug in the formula

In-line CAM charges = 4,000,000 ÷ 1,300,000

In-line CAM charges= $3.08

Therefore the amount that in-line tenants have to pay per square foot will be $3.08 per square foot.

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