Question

Math of Finance

You decided to quit smoking today.

*basic information* Now that you are going to save 200 €/month, you decided to save those 200€ per month in a bank account that offers a 3% interest rate compounded monthly, till the day you retire (that is to say, in 20 years)

If you decide to do your deposits at the end of every month (your first deposit will be in one month from today) in a bank account that offers a 3% interest rate compounded monthly, and the deposits will increase in a 0.1% month after month, and you keep on doing so for the next 20 years:

a) Draw the timeline (at least the first five periods) with its corresponding numeration of periods and cashflows in their corresponding points

b) How much money will you have at the end? Show the workout

c) What would happen if the growth rate and the interest rate is the same?

Answer #1

This is an example of a growing annuity. And we are required to find the future value of the following growing annuity.

**a) Timeline (at least the first five periods) with its
corresponding numeration of periods and cashflows in their
corresponding points**

**b) Future value of Growing Annuity
= **

FVGA = C1* [((1+r)^n - (1+g)^n) / (r-g)]

C1 = 200

r (3%) = 0.0025 (3/12)

g = 0.001

n = 240 (12*20)

Therefore, FVGA will be :

200 * [((1+0.0025)^240 - (1 + 0.001)^240) / (0.0025 - 0.001)] =
**73287.77**

**c)** If the growth rate and interest rate are
equal then the equation won't work as both the rates would offset
each other in the timeline and cashflow would be undefined.

You decided to quit smoking today.
Now that you are going to save 100 €/month, you decided to save
those 100€ per month in a bank account that offers a 5% interest
rate compounded monthly, till the day you retire (that is to say,
in 20 years). Please answer the following questions:
If you do your deposits at the end of every
month (so your first deposit will be in one month from today) in a
bank account that offers...

You take out a $25,000 30 years mortgage with monthly payments
and a rate of 3.5%, monthly compounded. What is your monthly
mortgage payment?
You take out a $25,000 30 years mortgage with monthly payments
and a rate of 3.5%, monthly compounded. What is the loan balance by
the end of year 15?
Calculate the future value at the end of year 4 of an
investment fund earning 7% annual interest and funded with the
following end-of-year deposits: $1,500 in...

You would like to save annually for buying a car 6 years from
today. Suppose the first deposit is made today and the last deposit
will be made 5 years from now. Assume the car will cost you $30,000
and your deposits earn you interest at 6% p.a, compounded
annually.
(a) What is your annual deposit amount?
(b) Instead of making annual deposits, you would like to make
your deposit monthly and the bank is happy to pay your interest...

You have decided to place $972 in equal deposits every month at
the beginning of the month into a savings account earning 14.83
percent per year, compounded monthly for the next 12 years. The
first deposit is made today. How much money will be in the account
at the end of that time period?
Round the answer to two decimal places.

You have decided to place $361 in equal deposits every month at
the beginning of the month into a savings account earning 4.63
percent per year, compounded monthly for the next 5 years. The
first deposit is made today. How much money will be in the account
at the end of that time period? Round the answer to two decimal
places.

You have decided to place $644 in equal deposits every month at
the beginning of the month into a savings account earning 5.88
percent per year, compounded monthly for the next 6 years. The
first deposit is made today. How much money will be in the account
at the end of that time period?
Round the answer to two decimal places.

you
decided to place $430 in equal deposits every month at the
beginning of the month into a savings account earning 7.22 percent
per year,compounded monthly for the next 6years.the first deposit
is made today.how much money will be in account at the end of that
time period?

You decided to save money for a travel to Barcelona in two
years. You decided to open a savings account and make equal monthly
deposits for the next two years. You think that you need to save
$5,000. You checked a few banks to find out the best savings
account and identified one, the APR of which is 3.6%. You will
receive interests every month and you are going to keep those
received interests in your savings account. How much...

You have decided to begin saving for a vacation to Hawaii. You
believe that the full cost of the vacation, with airfare,
accommodations, and dining will be $5,000. You are going to begin
saving $150 per month, beginning one month from today. If your
account pays interest at a rate of 7.2% APR compounded monthly, how
many months will it take to save $5,000? Round your answer UP to
the nearest whole month.

You buy a car for $30,000 and are going to finance it over 6
years. The dealership make you two offers. You can either have 0%
interest for the first 3 years and a nominal annual rate of 6%
compounded monthly for the last 3 years or you can have a nominal
annual rate of 3% compounded monthly for all 6 years. In either
case you are expected to make monthly payments at the end of each
month for the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 16 minutes ago

asked 18 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago