SOLUTION: Beginning at age 30, Yoshi paid $400 per month into an ordinary annuity that paid 5.3% interest. As retirement age approached, Yoshi wanted to know the amount of the annuity at sev

Question 1150337: Beginning at age 30, Yoshi paid $400 per month into an ordinary annuity that paid 5.3% interest. As retirement age approached, Yoshi wanted to know the amount of the annuity at several different ages to help plan when to retire. Help Yoshi by finding the amount of the annuity when Yoshi is the following ages. (Round your final answer to two decimal places.)

(a) 65 years old
(b) 66 years old
(c) 67 years old
(d) 68 years old
(e) 69 years old
(f) 70 years old

Answer by ikleyn(52834) (Show Source): You can put this solution on YOUR website!
.


I will assume that Yoshi deposits $400 at the end of each month.
Then it is a classic Ordinary Annuity saving plan. The general formula is 


    FV = ,    (1)


where  FV is the future value of the account;  P is the monthly payment (deposit); r is the monthly percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 12, in this case).


Under the given conditions, P = 400;  r = 0.053/12.  Starting from the age of 30 years to the end of 64-th years 
(to the 65-th birthday) n = 35 years and  12*35 = 420.  So, according to the formula (1), at the end of the 64-th year 
(to the 65-th birthday) the amount at the account is 


    FV =  =  = $485945.21.    ANSWER


To any other birthday, calculate the future value at the account by the same way.

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On Ordinary Annuity saving plans, see the lessons
- Ordinary Annuity saving plans and geometric progressions
- Solved problems on Ordinary Annuity saving plans
in this site.

The lessons contain EVERYTHING you need to know about this subject, in clear and compact form.

When you learn from these lessons, you will be able to do similar calculations in semi-automatic mode.

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