SOLUTION: I want to accumulate $120,000 in 30 years. Plan A is a single deposit into an account that compounds annually and an apr of 5% plan B is a single deposit into an account with conti

Question 846572: I want to accumulate $120,000 in 30 years. Plan A is a single deposit into an account that compounds annually and an apr of 5% plan B is a single deposit into an account with continuous compounding and an apr of 4.8%
How much do I need to deposit into each account in order to reach my goal
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you want $120,000 in 30 years.
plan A compounds annually at an apr of 5%.
plan B compounds continuously at an apr of 4.8%

the formula for annual compounding is:
f = p * (1+r)^n

f is the future value which is equal to 120,000
p is the present value.
r is the interest rate per time period.
n is the number of time periods.

since the compounding is annually, than the interest rate is the apr divided by 100 which is equal to .05.
since the time periods are annual, then the number of time periods is the same as the number of years which is equal to 30.

the formula becomes:

120,000 = p * (1.05)^30.
divide both sides of this formula by (1.05)^30 to get:
120,000 / (1.05)^30 = p which makes p equal to $27,765.29.

that's what you'd have to invest today at 5% compounded annually in order to have $120,000 thirty years from now.

the formula for continuous compounding is:
f = p * e^(r*n)

r is the interest rate per time period which is in years.
n is the number of time periods which is in years.

the formula becomes:

120,000 = p * e^(.048 * 30).
divide both sides of this equation by 3^(.048 * 30) to get:
120,000 / (e^(.048*30)) = p which makes p equal to 28,431.33.

that's what you'd have to invest today at 5% compounded continuously in order to have $120,000 thirty years from now.

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