Question

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.

Answer 1

Answer:

X=17,384.37

Step-by-step explanation:

The present value of the perpetuity can be calculated by discounted for the different interest rates:

$PV_{perpetuity}=[\frac{1}{0.1}+\frac{(\frac{1}{0.08}-\frac{1}{0.1})}{1.1^{10}}]\times 15,000+15000\\\\\\=164,457.87+15,000=179,457.87$

#Now, we use the annuity-due present value factor to get the present values of the annuity payments, let X be the annual annuity payments;

$X[\ddot a_{10}_|_{0.10}+\frac{\ddot a_{15}|_{0.08}}{1.10^{10}}]=179,457.87\\\\\\X[6.759+\frac{9.244}{1.1^{10}}]=179457.87\\\\\\X=17384.37$

Hence, the value of X is 17,384.37