Question

A life insurance company invests ​$9000 in a bank account in order to fund a death benefit of ​$81,000. Growth in the investment over time can be modeled by the differential equation​ below:

dA/dt = Ai
where i is the interest rate and​ A(t) is the amount invested at time t​ (in years).
(A) Calculate the interest rate that the investment must earn in order for the company to fund the death benefit in 24 years.

Answer 1

Interest rate is 9.59%

Explanation:

The interest rate the investment must earn in order that the death benefit could of $81,000 in 24 years' time can be derived from the rate formula in excel spreadsheet.

=rate(nper,pmt,-pv,fv)

nper is the number of years the $9,000 would be invested for i.e 24 years

pmt is the periodic additional investment which is zero

pv is the amount invested today i.e $9000

fv is the amount of death benefit payable in 24 years' time that is $81000

=rate(24,0,-9000,81000)=9.59%