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.

Question

Amiya Mathews

Mathematics

22 September, 16:10

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.

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Answers (1)

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Skinner · Answer 1

Interest rate is 9.59%

Step-by-step 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%