Compound interest compounding semi annualy?

Question

Hi Could someone help me solving this problem , Matt has just won $100000 in the lottery and has decided to go into semi retirement . His wife told Matt that by investing his winnings in an account that pays 12% semi annually compounding interest , he can generate a regular income for the next 20 years . If matt invests the whole $100000 in this account how much will each payment be that he receives.

Answer 1

If he were to invest the $100,000 and just receive an interest payment every six months, then he would get 6% of it every six months. That is $6,000 -- not $60,000 as someone else said.

However, if he wasn an annuity that pays the same amount every six months, then he will get more -- because he is also getting a principal payment each time.

The present value of an annuity is given by the following formula:

PV = A/R - A/(R*(1+R)^N)

Here PV = $100,000
R = 6% (the one period interest rate -- half of 12%)
N = 40 -- since there are 40 semiannual payments.
A = amount of payment.


Do the algebra, and you find that A = $6,646.15

Answer 2

I assume by your question that he is going to draw down the principal over 20 years so that at the end of 20 years all money will be gone. But you did not specify how often the "regular income" will be received, monthly, semi-annually, or annually.

For simplicity I will assume semi-annually.

$6009.30 distribution every 6 months for 20 years. Total distribution $240,372.

Answer 3

Sundar:
At 12% semi-annual he will get $60,000 every 6 months. A 12% semi-annaul compounding is equivalent to 12.36% annual coumponding.

Thanks,
Kimi

Answer 4

this is a scam no account pays that much.Your 100 k will earn about 5 k year in interest in the treasury market.or cd at bank.

Answer 5

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