Question

(1 point) A bank account earns 11 percent interest compounded continuously. At what (constant, continuous) rate must a parent deposit money into such an account in order to save 100000 dollars in 13 years for a child's college expenses? rate = (dollars/year) If the parent decides instead to deposit a lump sum now in order to attain the goal of 100000 dollars in 13 years, how much must be deposited now? amount = (dollars)

Answer 1

a). Assuming deposits are made at the end of the years,

interest rate = 11% compounded continuously

So, Effective annual rate can be calculated using formula EAR = e^i - 1 = e^(0.11) - 1 = 11.63%

Using ordinary annuity formula to compute annual payment A

A= FV*r/((1+r)^t - 1) = 100000*0.1163/(1.1163^13 - 1) = $3658.04 dollars/year

b). let amount X is invested today,

Final value after 13 years = $100000

using formula FV = PV*e^(i*t),

PV = 100000*e^(-0.11*13) = $23930.89 dollars