Question

You are considering an investment by depositing $25,000 to an account today and making monthly contributions of $300 into the account for 10 years. If you want to have $100,000 in the account after 10 years, what annual interest rate must you earn from the account?

If you go ahead with the investment and decide to increase the monthly contribution to $400 after 5 years (deposit $25,000 today, $300 monthly for the first 5 years), how much will you have in the account at the end of 10 years.

Answer 1

1. PV of Deposit =25000
Number of Months =10*12 =120
PMT =300
FV in the account after 10 years =100000
Monthly Rate using Financial Calculator
N=120;PMT=-300;PV=-25000;FV=10000;CPT I/Y =0.560053891981734%

APR =12*0.56005% =6.72%

2. PV =25000
Number of Months =10*12 =120
PMT =300
FV in year 5 of the annuity =PMT*((1+r)^n-1)/r) =300*((1+0.560053891981734%)^60-1)/0.560053891981734%)
=21323.28669
FV in year 10 =FV of current Deposit+FV of Year 5 Value+FV of 400 value for last 5 years
=25000*(1+0.560053891981734%)^120+21323.28669 *(1+0.560053891981734% )^60+400*((1+0.560053891981734%)^60-1)/0.560053891981734%) =107107.76