What is the present value of a series of payments that grow by 10% per year over 5 years. The starting value is $50,000 at the end of year 1. The interest rate (discount rate) is 6%, compounded annually.

PV = $163,714.68

Explanation:

Giving the following information:

A series of payments grow by 10% per year over 5 years. The starting value is $50,000 at the end of year 1. The interest rate is 6%.

The easiest way is to include the growing rate in the interest rate, therefore:

Interest rate = 16%

First, we need to calculate the final value of the annuity and then the present value:

FV = {A*[ (1+i) ^n-1]}/i

A = annual deposit = 50,000

i = 0.16

n = 5

FV = {50,000*[ (1.16^5) - 1]}/0.16 = $343,856.77

Now, we can calculate the present value:

PV = FV / (1+i) ^n

PV = 343,856.77/1.16^5 = $163,714.68