investment

Question

a saver wants $100000 after 10 years and believes that it is possible to earn an annual rate of 8 percent on invested funds.  a what amount must be invested each year to accumulate $100000 if 1 the payments are made at the beginning of each year or 2 if they are made at the end of each year? b how much must be invested annually if the expected yield is only 5 percent?

Answer 1

a.1.)

 

10^5 = p (1.08)^10 + p (1.08)^9 + ... + p (1.08)^2 + p (1.08)

 

10^5 / 1.08 = p (1.08)^9 + p (1.08)^8 + ... + p (1.08) + p

 

10^5 - 10^5 / 1.08 = p (1.08)^10 - p = p ( (1.08)^10 - 1 )

 

p = ( 10^5 - 10^5 / 1.08 ) / ( (1.08)^10 - 1 )

 

p = 10^5 ( 1 - 1 / 1.08 ) / ( (1.08)^10 - 1 )

 

p = 10^5 ( 0.08 / 1.08 ) / ( (1.08)^10 - 1 )

 

p ≈ $6,391.62

 

b.1.)

 

p = 10^5 ( 0.05 / 1.05 ) / ( (1.05)^10 - 1 )

 

p ≈ $7,571.86