Question

7. Use the present value formula or the future value table to determine the rate of return for each
of the specified investments.
A. Assume an investment of$30,000 today is expected to mature in ten years with a value of
$59,010. What is the annual rate of return (r) that will be earned on this investment?

B. Assume a business is considering an investment of $20,000 that will grow to $36,000 in
eight years. The business requires a 7 percent annual rate of return on its investments.
Determine whether the business should make the investment by calculating its rate of
return.

8. Use the future value of an annuity table or formula to determine the future values in each of the
specified scenarios.
A. An ordinary annuity consists of payments of $1,000 received at the end of each year for five
years. Assume that each $1,000 payment will be deposited in an account that pays 4
percent interest annually. Using the future value of an annuity table or formula, determine
the annuity’s future value.

B. An organization’s risk management professional has determined that a steam boiler will
need to be replaced in three years. The total cost of the replacement at that time is
expected to be $75,000. The risk management professional wants to budget an equal
amount to be deposited into a reserve fund at the end of each of the next three years. The
fund is expected to earn a return of 3 percent, compounded annually. The risk management
professional knows the amount to be deposited will be less than $25,000 ($75,000/3 years)
because of the benefit of the 3 percent compounded interest. Using the future value of an
annuity formula and the future value table, determine how much must be deposited in the
account at the end of each of the next three years in order for it to accumulate to $75,000.

Answer 1

7.A.

We know present value = future value/(1+r)^n where r = Annual rate of return;n = 10 years

30000 = 59010/(1+r)^10

or, (1+r) = (59010/30000)^(1/10)

or, r = (59010/30000)^(1/10) - 1 = 0.069991767 = 6.9991767% [Which can be approximated to 7%]

B.

We know present value = future value/(1+r)^n where r = Annual rate of return;n = 8 years

20000 = 36000/(1+r)^8

or, r = (36000/20000)^(1/8) - 1 = 0.076239836 = 7.6239836% which is more than required rate of return so business should make the investment