Quantitative Problem 1: You plan to deposit $2,500 per year for 6 years into a m
ID: 2806218 • Letter: Q
Question
Quantitative Problem 1: You plan to deposit $2,500 per year for 6 years into a money market account with an annual return of 3%. You plan to make your first deposit one year from today. a. What amount will be in your account at the end of 6 years? Round your answer to the nearest cent. Do not round intermediate calculations. b. Assume that your deposits will begin today. What amount will be in your account after 6 years? Round your answer to the nearest cent. Do not round intermediate calculations.Explanation / Answer
1.a.
Formula for future value of ordinary annuity:
FV = P x [{(1+r)n -1}/r]
Where,
FV = Future value of ordinary annuity
P = Payment per period = $ 2,500
r = rate per period = 3 % or 0.03
n = no. of periods = 6
FV = $ 2,500 x [{(1+0.03)6 -1}/0.03]
= $ 2,500 x [{(1.03)6 -1}/0.03]
= $ 2,500 x [{(1.194052 - 1}/0.03]
= $ 2,500 x [(0.194052)/0.03]
= $ 2,500 x 6.46841 = $ 16,171.02
At the end of six years account balance will be $ 16,171.02
b.
Formula for future value of annuity due:
FV = P x [{(1+r)n -1}/r] x (1 +r)
Using the same values we as above get FV as:
FV = $ 2,500 x [{(1+0.03)6 -1}/0.03] x (1+0.03)
= $ 2,500 x [{(1.03)6 -1}/0.03] x (1.03)
= $ 2,500 x [{(1.194052 - 1}/0.03] x (1.03)
= $ 2,500 x [(0.194052)/0.03] x (1.03)
= $ 2,500 x 6.46841 x 1.03 = $ 16,656.16
At the end of six years account balance will be $ 16,656.16