Question

Sonata will receive $20,000 today (January 1, 2010), and also on each January 1^st for the next five years (2011 – 2015). Assuming a 5% interest rate, how much must be placed in the fund today to support Sonata’s withdrawals?

$________________________

$12,000 has been deposited annually starting on January 1, 2014. If the funds are earning 8% interest, what will the balance be on December 31, 2021?

$________________________

Answer 1

Periodic amount received today and thereafter each year for 5 year= $ 20,000

Interest rate = 5%

Calculating the present value of periodic payment using Present Value of Annuity:

Where, C= Periodic Payments = $ 20,000

r = Periodic Interest rate = 0.05

n= no of periods = 5

Present Value = $ 106,589.53

So, funds must be placed in today to support Sonata’s withdrawals is $ 106.589.53

b). Calculating the future value using Future value of Annuity due :

Where, C= Periodic Payments = $12,000

r = Periodic Interest rate = 0.08

n= no of periods = 8

future Value = $ 137,850.69

So, the balance be on December 31, 2021 is $137,850.69