# calculus

posted by .

What single deposit today in an account paying 7% interest compounded continuously would yield \$18500 in 10yr?

• calculus -

r = interest percent/100
dy/dt = r y
y = a e^kt
dy/dt = ak e^kt = r a e^kt
r = k
so
y = a e^rt
note when t = 0, y = a the original deposit
18500 = a e^(.07*10)
ln (18500/a) = .7
ln 18500 - ln a = .7
9.83 - .7 = ln a
ln a = 9.1255
a = 9186.83

check y = 9187 e^(.7)
y = 18500 check

## Similar Questions

1. ### math

how would you write an equaton if you deposit \$3200 into an account that earns 6.2% interest, compounded continuously?
2. ### calculus

3. A deposit of ___(i)___is made into an account paying an interest rate of 5% compounded annually. How many annual payments of ___(iii)___can be made from this account?
3. ### Finance

You can deposit 10,000 into an account paying 9% annual interest either today or exactly 10 years from today. How much better off will you be at the end of 40 years if you decide to make the initial deposit today rather than 1o years …
4. ### algebra

\$7,000 is invested into two accounts: 4,000 into an account paying 5% interest compounded monthly and \$3,000 into an account paying 4.1% interest compounded continuously. compute the total interest earned at the end of 2 years.
5. ### finance

14. Assume Julian has a choice between two deposit accounts. Account A has an annual percentage rate of 7.55 percent but with interest compounded monthly. Account B has an annual percentage rate of 7.45 percent with interest compounded …
6. ### math

you deposit \$2200 in an account that pays 3% annual interest. after 15 years, you withdraw the money. what is the balance if the interest is compounded continuously?
7. ### math

you deposit \$2200 in an account that pays 3% interest, after 15 years you withdraw, what is the balance if the interest is compounded continuously
8. ### Algebra ASAP

Suppose that \$17,000 is invested in a savings account paying 5.1% interest per year. (a) Write the formula for the amount A in the account after t years if interest is compounded monthly. A(t) = (b) Find the amount in the account after …
9. ### PRE-CALCULUS

. Sam won \$150,000 in the Michigan lottery and decides to invest the money for retirement in 20 years. Find the accumulated value for Samâ€™s retirement for each of his options: (a) a certificate of deposit paying 5.4% compounded yearly …
10. ### Calculus

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?

More Similar Questions