Question

One person made regular deposits with a financial institution for 15 years. In the first 5 years, deposits were made in the final amount of 2,000 euros. In the next 10 years, deposits will be 200 euros at the end of each month. Calculate a rate of 20% per annum with semi-annual capitalizations, or the accumulated amount collected on the day you made your last deposit.

Answer 1

Effective Annual Rate =(1+20%/2)^2-1 =21%
PMT=2000 for first 5 years
Number of Periods =5
FV of first 5 annuities at year 5=PMT*((1+r)^n-1)/r =2000*((1+21%)^5-1)/21%=15178.4996

For next 10 Years PMT =200
Number of months =10*12 =120
Effective Annual Rate =(1+20%/2)^(1/6)-1=1.60118677733874%
FV of annuities in last 10 years =PMT*((1+r)^n-1)/r) =200*(((1+1.60118677733874%)^120-1)/1.60118677733874%)
=71540.6851

Amount accumulated at end of 15th year =FV of first 5 annuities at year 5*(1+21%)^10+FV of annuities in last 10 years
=15178.4996*(1+21%)^10+71540.6851= 173654.04