Lloyd Blankfein would like to supplement his low pension paid by his employer Go

Question

Lloyd Blankfein would like to supplement his low pension paid by his employer Goldman Sacks. His personal banker Jamie Dimon told him that he could pay $1,000 every month for ten years (making 10 × 12 = 120 payments at the end of each month until her retirement) and then he will start receiving $1,000 forever. He will receive the first $1,000 in ten years and one month, i.e. one month after he made his last payment; after he passes away his heirs (and their heirs etc.) will continue to receive the monthly payments forever. What is the effective annual rate (EAR) the bank used to calculate the terms of this deal?

Please state all formulas used

Show me the step by step process & calculations

I will show you how I started it off ....

$1,000 every month for 10 years

12 x 10 = 120 months

so for the first 120 months, he will get $1,000 each month

and during month 121 he will get 1,000 forever

is this with EAR kept in mind? Please help

I also have another question that is similar to this question, may you please help me solve it?

I will show the steps that I used to start the question, but then I got stumped.

Honest Joe’s Used RVs offers the following payment options for a used 2010 Freedom 314SO:

1. $49,900 in cash today;

2. $20,000 down payment right now and then pay $1,500 monthly for the next two years (i.e., 24 payments of $1,500 with the first payment due one month from today).

What effective annual interest rate (EAR) is he charging in the second payment option? Note: You can use the IRR function or Goal Seek (or Solver) in Excel to solve this problem.

PV option 1 ($49,900) = PV option 2

t=0 = $20,000

t=1 = $1,500

t=2 ............ t=24 = $1,500

n = 24

PMT = $1,500

EAR (r) = ?

PLEASE help me solve both questions!!!! I have a quiz tomorrow and I would like to know how these are both solved. PLEASE use step by step calculations..

THANK YOU SO MUCH IN ADVANCE! :D

Explanation / Answer

(1)

The key to solving this is to understand the equvalence:

Future value of $1,000 monthly payment for 10 years, at end of 10 years = Present value of the perpetual stream of income ($1,000 per month) starting month 121, continuing forever.

(a) Future value of $1,000 monthly payment for 10 years, at end of 10 years

= $1,000 x Future value interest factory of annuity (r%, 120 months)

Where future value interest factory of annuity (r%, N months) = [(1 + r)N - 1] / r

(b) Present value of the perpetual stream of income ($1,000 per month) starting month 121, continuing forever

= $1,000 / r

Equating both values,

$1,000 x [(1 + r)N - 1] / r = $1,000 / r

So, [(1 + r)N - 1] = 1

(1 + r)N = 1 + 1 = 2

(1 + r)120 = 2

Taking logarithms of each side:

120 log (1 + r) = log 2 = 0.3010

log (1 + r) = 0.3010 / 120 = 0.0025

(1 + r) = e0.0025

So, (1 + r) = 1.002503

r = 1.002503 - 1 = 0.002503

Or, r = 0.2503%

This is the monthly interest rate. So, annual interest rate = (0.2503% x 12) = 3%

(2)

Here, the equivalence is:

49,900 = $20,000 + [$1,500 x Present value interest factor of annuity (r%, N periods)]

Or, $1,500 x Present value interest factor of annuity (r%, N periods) = $29,900

Using a financial calculator, input following values to obtain r:

PMT = - 1,500

PV = 29,900

N = 24

[CPT] [I/Y]

You'll get [I/Y] = 1.5419

So, r = 1.5419%

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