Question

A 20 year old started saving and investing $300 per month and had a 7% growth rate, by the time they would retire they would have over $1,000,000 saved. This assumes that they plan to retire at age 66 and are able to invest every month at the $300 per month rate. The total amount the client would save and invest just over $165,000 and the remainder is due to the compounding interest associated with the investment earnings.

Draw this or explain please

Answer 1

Note: It is assumed that growth rate i.e. Interest Rate of 7% is Monthly Compounded.

FV of Annuity = P*[{(1+i)^n}-1]/i

Where, P = Annuity = 300, i = Interest Rate = 0.07/12 = 0.005833, n = Number of Periods = (66-20)*12 = 552

Therefore, FV = 300*[{(1+0.005833)^552}-1]/0.005833 = 300*23.795066/0.005833 = $1223746.27

Amount ACTUALLY DEPOSITED = Annuity Amount*Number of Months = 300*552 = $165600

Explanation:

As calculated above, the TOTAL amount that we ACTUALLY DEPOSITED over all 46 years or 552 months is $165600, BUT, because of the interest and compounding of interest, the TOTAL BALANCE at the end is $1223746.27.

In 1st month, amount deposited will be $300

Interest earned for 1st month will be 300*0.005833 = $1.75

In 2nd month, amount deposited will be $300

Interest earned for 2nd month will be on TOTAL BALANCE i.e. 2 months deposits + INTEREST OF 1st month i.e. (600+1.75)*0.005833 = $3.51

This will keep on and on till all 552 payments.

Initially, for few months it won't make much difference. BUT, after a while, say after 100 months, the interest will be earned on all 100 deposits AND ON TOTAL INTEREST EARNED FOR 100 MONTHS.

This Compounding will go on and on, and the INTEREST ON INTEREST PORTION will Increase way beyond the Total Deposited Amount.

Due to this, Although actual amount deposited is just over $165000, but actual balance at the end is over $1 Million.