Evelyn starts a retirement fund 10 years before retirement S

Evelyn starts a retirement fund 10 years before retirement. She pays $200 per month into the annuity for 10 years. Her total investment is $24,000. Esther starts a retirement fund 20 years before retirement. She pays $100 per month into the annuity for 20 years. Her total investment is $24,000. Lois starts a retirement fund 30 years before retirement. She pays $50 per month into the annuity for 30 years. Her total investment is $18,000. In each case the annuities pay 6% interest compounded monthly. (a) Find the value of each annuity at the time of retirement. (Round your final answer to two decimal places.) Evelyn $ Esther $ Lois $ (b) What lesson should be learned from the answers in part (a)? Start your savings program early for the best return. Evelyn will have the most money for retirement. There is always enough time to start your savings program. Esther will have the most money for retirement.

Solution

a) Use the future value annuity formula :

FV = C*[( 1+i)^n -1 ]/i

where C = Cash flow per period

i = interest rate

n = number of payments

Evelyn : C = $200 ; n = 10*12 = 120; i =0.06/12 =0.005

FV= 200[ (1 +0.005)^120 - 1 ]/0.005

= $ 32775.87

Esther : C = 100 ; n= 20*12 = 240 ; i = 0.005

FV = 100[(1+0.005)^240 -1 ]/0.005

= $ 46204.09

Lois : C = 50 ; n =12*30 = 360 ; i = 0.005

FV = 50[ (1+0.005)^360 -1 ]/0.005

=$ 50225.75

Lois invested least and got maximum returns on her savings

b) It is found that we should start investing as early as possible even with a small amount.