Financial Maths Qs

Take Your Pants Off

Question:
Jack plans to deposit 3000 every month in a account with an AER of 7.6%. How much will be in the account after 4 years, continuously compounded.

My method: (1+7.6%)^1/12 -1 =6.122x10^-3

3000 x (1+6.122x10^-3)^48 -1 OVER 6.122x10^-3
=166,080

Is this correct ?

Thanks in advance.

Molly

Take Your Pants Off wrote: »

Question:
Jack plans to deposit 3000 every month in a account with an AER of 7.6%. How much will be in the account after 4 years, continuously compounded.

My method: (1+7.6%)^1/12 -1 =6.122x10^-3

3000 x (1+6.122x10^-3)^48 -1 OVER 6.122x10^-3
=166,080

Is this correct ?

Thanks in advance.

This is not continuous compounding, it's just monthly compounding. Continuous compounding involves an exponent.

Take Your Pants Off

Molly wrote: »

This is not continuous compounding, it's just monthly compounding. Continuous compounding involves an exponent.

Thanks for replying.
I don't get it, its a fv ordinary annuity yes, first we get the monthly compounding, i, for this. Which I did, then I got the future value of this.

Molly

You calculated an effective monthly interest rate for compound interest. Compound interest as you know calculates interest on interest at set periods. Continuous compounding calculates interest every second (hence continuous) you don't use the (1+i)^t formula, you use e^(i*t). You need to calculate a different I for continuous compounding

http://www.moneychimp.com/articles/finworks/continuous_compounding.htm

Take Your Pants Off

Molly wrote: »

You calculated an effective monthly interest rate for compound interest. Compound interest as you know calculates interest on interest at set periods. Continuous compounding calculates interest every second (hence continuous) you don't use the (1+i)^t formula, you use e^(i*t). You need to calculate a different I for continuous compounding

http://www.moneychimp.com/articles/finworks/continuous_compounding.htm

Ah ok, CHEERS !

Take Your Pants Off

Like this you mean?
I get 167753.

Yakuza

To convert an AER of i% p.a. to a continuously compounded rate, you use ln(1+i).

I got answers of €167,827.94 and €166,806.61 (depending on whether the money is paid at the start of the month or at the end - i.e. does the first payment accumulate for 48 or 47 months and the last for 1 or zero month(s) etc).

The 7.6 in your answer needs to be replaced by 0.073250462 - ln (1.076).

1000 invested for a year at 7.6% AER will accumulate to €1,076.
1000 invested for a year at 7.3250462% (continuously compounded) will also accumulate €1,076 (1000 * e^(0.073250462)).