Cosmos Touring wishes to replace its luxury bus in 10 years by accumulating funds in a special account. The new bus is expected to cost $180,000. How much must Cosmos put into the fund in equal, end-of-year amounts if earnings are expected to be 8% for the first 4 years and 10% thereafter?

A) $12,107
B) $11,465
C) $9,901
D) $14,727

Question

Gagandeep Singh Dhaliwal · Accepted Answer

Final Answer : B, Explanation :  To calculate the amount that Cosmos needs to put into the fund each year, we can use the future value of an annuity formula:FV = PMT x [(1 + r)n - 1]/rWhere:PMT = the annual paymentr = the interest raten = the number of yearsFor the first four years, the interest rate is 8%, so we plug in the values:$180,000 = PMT x [(1 + 0.08)^4 - 1]/0.08$180,000 = PMT x 3.312133PMT = $54,324.61So, Cosmos needs to put $54,324.61 into the fund at the end of each year for the first four years.After the fourth year, the interest rate increases to 10%. To calculate the amount needed each year, we use the same formula with different values:$180,000 = PMT x [(1 + 0.10)^6 - 1]/0.10$180,000 = PMT x 7.355271PMT = $24,457.32So, Cosmos needs to put $24,457.32 into the fund at the end of each year for the next six years.To check if this is the correct answer, we can calculate the present value of the annuity and see if it matches the cost of the bus:PV = PMT x [(1 - (1 + r)^-n)/r]For the first four years:PV = $54,324.61 x [(1 - (1 + 0.08)^-4)/0.08]PV = $179,999.94And for the next six years:PV = $24,457.32 x [(1 - (1 + 0.10)^-6)/0.10]PV = $179,999.84The total present value of the annuity is $359,999.78, which is close to the cost of the bus ($180,000 x 2 = $360,000).The option with the closest answer is B) $11,465, which is the annual payment for the entire 10 years. So, the answer is B) $11,465.

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