Question

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.

Answer 1

To calculate the present value of a series of payments growing by 10% per year over 5 years with a 6% discount rate, apply the present value of a growing annuity formula to each year's payment and sum the values. This financial calculation will give the total present worth of the payment stream.

Step-by-step explanation:

The question pertains to the calculation of the present value of a series of future payments that are increasing at a constant rate. Specifically, it involves calculating the current worth of payments that start at $50,000 and grow by 10% annually over 5 years, using a discount rate of 6%. To solve this problem, we must apply the present value of a growing annuity formula for each payment and then sum these values to obtain the total present value of the payment series.

Calculations for Present Value of a Growing Annuity:

For each year (t), calculate the present value (PVt) using the formula:

PVt = Payment at year t / (1 + discount rate)^t

Where the payment at year t is the previous year's payment increased by 10%. Sum all PVt values from year 1 to year 5 to obtain the total present value of the annuity.

Answer 2

PV= $163,714.68

Step-by-step 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