Mathematics, 18.03.2020 18:37 gudon986732
Jack inherited a perpetuity-due, with annual payments of 15,000. He immediately exchanged the perpetuity for a 25-year annuity-due having the same present value. The annuity-due has annual payments of X. All the present values are based on an annual effective interest rate of 10% for the first 10 years and 8% thereafter. Calculate X.
Answers: 2
![PV_{perpetuity}=[\frac{1}{0.1}+\frac{(\frac{1}{0.08}-\frac{1}{0.1})}{1.1^{10}}]\times 15,000+15000\\\\\\=164,457.87+15,000=179,457.87](/tpl/images/0552/3264/78de6.png)
![X[\ddot a_{10}_|_{0.10}+\frac{\ddot a_{15}|_{0.08}}{1.10^{10}}]=179,457.87\\\\\\X[6.759+\frac{9.244}{1.1^{10}}]=179457.87\\\\\\X=17384.37](/tpl/images/0552/3264/1a887.png)
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Jack inherited a perpetuity-due, with annual payments of 15,000. He immediately exchanged the perpet...
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