Period | Contribution | Balance |

Kevin deposited an amount of **$2,000** in a bank paying an annual interest rate of **2.5%**, compounded **quarterly**. How much money will Kevin have after **8 years**?

__Solution:__

**P** = 2,000

**r** = 0.025

**n** = 4

**t** = 8

**A** = 2,000 * (1 + 0.025/4)^(4*8)

**A** = 2,441.29

Joe deposited an amount of **$5,000** in a bank paying an annual interest rate of **3.3%**, compounded **annually**. Everytime at the END of the month, he put in an additional **$160**. How much money will Joe have after **15 years**?

__Solution:__

**P** = 5,000

**PMT** = 160

**r** = 0.033

**n** = 1

**t** = 15

**CI** = 5,000 * (1 + 0.033/1)^(1*15)

**CI** = 8,137.20

**FV** = 160 * (((1 + 0.033/1)^(1*15) - 1) / (0.033/1))

**FV** = 3,042.13

**A** = 8,137.20 + 3,042.13

**A** = 11,179.33

By An Do

11/25/2016

11/25/2016

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A = P * (1 + r/n)^(nt)

**A** = Amount of money accumulated after n years, including interest

**P** = Principal investment amount (the initial deposit or loan amount)

**r** = Annual rate of interest (as a decimal)

**n** = Number of times the interest is compounded per year

**t** = Number of years the amount is deposited or borrowed for

A = CI + FV

CI = P * (1+r/n)^(nt)

If the additional deposits are made at the END of the period (end of month, year, etc):

FV = PMT * (((1 + r/n)^nt - 1) / (r/n))

If the additional deposits are made at the BEGINNING of the period (beginning of month, year, etc):

FV = PMT * (((1 + r/n)^nt - 1) / (r/n)) * (1+r/n)

**A** = Amount of money accumulated after n years, including interest

**P** = Principal investment amount (the initial deposit or loan amount)

**PMT** = The additional payment every n months

**r** = Annual rate of interest (as a decimal)

**n** = Number of times the interest is compounded per year AND additional payment frequency

**t** = Number of years the amount is deposited or borrowed for

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