You need $12,000 in your account 5 years from now and the interest rate is 6% per year, compounded continuously.
How much should you deposit now?
Can someone explain the steps of solving this to me, please?
instantaneous compounding implies:
amount = deposit x e^(rt) , where r is the rate expressed as a decimal
so
amount = 12000(e^(.06)(5))
= 12000 e^.3
= ...
you have a function key on your calculator which does e^x , it is usually the 2nd function key of ln x
To solve this problem, you can use the formula for compound interest when it is compounded continuously:
A = P * e^(rt)
Where:
A is the final amount (in this case, $12,000)
P is the principal amount (the initial deposit)
e is the mathematical constant approximately equal to 2.71828
r is the annual interest rate (6% per year, so r = 0.06)
t is the number of years (5 years)
You need to find out how much you should deposit now (P). Let's rearrange the formula:
P = A / e^(rt)
Now, substitute the given values into the formula:
P = 12000 / e^(0.06 * 5)
To calculate e^(0.06 * 5), you can use a scientific calculator or computer program:
e^(0.06 * 5) ≈ 1.3480082
Now, substitute this value back into the formula:
P = 12000 / 1.3480082
P ≈ $8896.86
Therefore, you should deposit approximately $8896.86 now to have $12,000 in your account 5 years from now with an interest rate of 6% compounded continuously.