How much money would you have after 10 years if you deposite

How much money would you have after 10 years if you deposited $5000 in an account that compounds monthly and earns you 2% APR the first year, 5% APR for the next 4 years, and 10% APR for the remaining 5 years?

Solution

With monthly compounding,

2% APR = (2/12) = 0.17% per month for 12 months

5% APR = (5/12) = 0.42% per month for 48 months

10% APR = (10/12) = 0.83% per month for 60 months

Future value (FV) after 1st year = $5,000 x (1.0017)¹² = $5,000 x 1.0206 = $5,103

FV of this amount after another 4 years = $5,103 x (1.0042)⁴⁸ = $5,103 x 1.2228 = $6,240

FV of this after another 5 years = $6,240 x (1.0083)⁶⁰ = $6,240 x 1.6420 = $10,246

So FV after 10 years = $10,246