Lesson Annual depositing and semi-annual compounding in ordinary annuity saving plan

Annual depositing and semi-annual compounding in ordinary annuity saving plan

Problem 1

The situation is close to ordinary annuity account, but there is some difference.
Since the account is replenished once per year, but is compounded twice per year (semi-annually),
we should and we can use the scheme of the annually deposited and annually compounded ordinary annuity
with the EFFECTIVE annual multiplicative growth rate of   = 1.092025.


So, we use the formula for the future value of the ordinary annuity 

    FV = ,   


where  FV is the future value of the account;  P is annual payment (deposit); 
r is the annual effective percentage rate presented as a decimal; 
n is the number of deposits (= the number of years, in this case).


From this formula, you get for for the annual payment 


    P = .     (1)


Under the given conditions, FV = 57,500,000;  r = 0.092025;  n = 7.  
So, according to the formula (1), you get for the annual payment 


    P =  = 6,211,008.91.


Answer.  The necessary annual deposit value is TZS 6,211,008.91 .