QMA - Present value/future value ANNUITY (1 Viewer)

[magik22]

I'm sure for the majority of people, they can differentiate when to use future and present value formula for an annuity but I have trouble.

The formula for present value(ordinary) of an annuity:

1-[(1+r)^-n]
A= R. -------------
r

where R = regular payments at the end of each payment period for 'n' payments with interest rate 'r' per period

The formula for future value (ordinary) of an annuity:

[(1+r)^n] - 1
A= R. --------------
r

An Ordinary Annuity is one where payments are made AT THE END of period rather than at the beginning (annuities due)

I will present two separate examples which are similar but one example requires using present value formula whilst the other requires future value formula.

Example 1

Suppose you are considering purchasing a car. The model you want will cost you $13,450. You have access to a loan through your bank, who would charge 9.50% interest. What would the monthly repayments be if the term of the loan was 5 years?


Example 2

Suppose you gain access to a bank that is offering a 7.5% interest (compounded monthly) savings account which you can depoist fixed amount into every month. If you need the account to contain $6500 in 4 years time, what would the monthly (end of month) deposits be?




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According to the lecturer, example 1 requires present value whilst example 2 requires future value formula.

The problem I have right now is differentiating between when to use present value formula and when to use future value formula.

Obviously, there are questions where you can tell immediately when to use the formulas - 'suppose you put $100 at the end of each month into a savings account which pays 5.5% accumulated monthly. What would the size of the account be after 45 years?' - thats obviously future value (ordinary annuity)

However with questions like examples 1 and 2....how would I differentiate? Are there keywords or the order of these words I should recognise?

Thank you for your time.

 

[wrong_turn]

example 1

well logically you will need the money in the present in order to pay for the car.
therefore pv = 13 450, r= 0.095/12, t= 12 x 5 =60 periods. find R.

example 2

this one you dont have the money now and you want the money in the future to amount to 6500 in 4 years time.

similar to the above example. work the rest out..cant be bothered to myself -___-

 

[08er]

Example 1 - you want to purchase the car NOW and to do this NOW, you'll need to borrow the full sum from the bank (called a loan), i.e. the present value formula.

Example 2 - "If you need the account to contain $6500 in 4 years time": this means you need the money in the FUTURE, i.e. future value formula.

For present/future values, just read the question carefully and try to understand WHEN the funds are needed.