Question

b) At the end of five years, how much is an initial $500 deposit followed by five year- end, annual $100 payments worth, assuming a compound annual interest rate of (i) 10%?
(ii) 5%? [6 pts]
c) At the end of six years, how much is an initial $500 deposit followed by five year-
end, annual $100 payments worth, assuming a compound annual interest rate of (i) 10%? (ii) 5%? [6pts]

Answer 1

Using the future value of annuity formula we can calculate the future value at end of the years.
Future value	Annual payment*((1+r)^n-1)/r)
bi)
Calculation of future value at 10% is shown below
Future value	500*(1.10^5)+100*((1.10^5)-1)/0.10)
Future value	805.255+(100*6.1051)
Future value	$1,415.77
ii)
Calculation of future value at 5% is shown below
Future value	(500*(1.05^5))+100*((1.05^5)-1)/0.05)
Future value	638.14+100*5.525631
Future value	$1,190.70
ci)
Calculation of future value at end of six years for 10% interest rate is shown below
Future value	1415.77*(1.10^1)
Future value	$1,557.34
ii)
Calculation of future value at end of six years for 10% interest rate is shown below
Future value	1190.70*(1.05^1)
Future value	$1,250.24