Question

John plans to invest $200 at the end of every quarter for next 2 years. Assume that today is January 1st, 2020. He expects to earn 10% annual rate of return with monthly compounding.

2.a Calculate the interest rate to be applied

2.b Calculate the future value at the end of 2 years (December 31st, 2021)

2.c Calculate the present value as on today (January 1st, 2020)

Answer 1

Ans 2a.
Given interest rate 10% pa with monthly compounding.
EAR =(1+10%/12)^12-1=10.4713% pa
Quarterly Effective Interest rate =10.4713%/4=2.618% per Qtr
So Interest rate to be applied is 2.618% per Qtr.
Ans 2b.
Formula for future value of Ordinary Annuity :
FV= A [ {(1+k)n-1}/k]
FV = Future annuity value
A = periodical investment=$200 per Qtr
K=interest rate=2.618% per Qtr
N=periods=2 years =8 Qtrs
FV =200*[(1.02618^8-1)/2.618%]
FV =$1754.54
So Future value of the Annuity after 2 yrs=$1,754.54
Ans 2c.
Formula for present value of an anuuity = PV= A [ {(1+k)n-1}/k(1+k)n]
PV = Present value of Annuity
A = periodical investment=$200 per Qtr
K=interest rate=2.618% per Qtr
N=periods=2 years =8 Qtrs
PV =200*[(1.02618^8-1)/(2.618%*1.02618^8)
PV =$1,426.84
So Present value of Annuity today =$1,426.84