Question

 

a. You have saved up for retirement in an annuity account. This account earns a return of 7% on annual basis but compounded monthly. You are due to retire in 6 years from now. You will receive monthly payments of $2,400 at the end of each month after retiring, for 15 years. How much have you saved up in this account today?

b. Two banks are competing to give a loan to you for $150,000 with 30-year term to maturity, bank a is offering 6% with quarterly compounding while bank b is offering 5.98% with daily compounding. Which bank should you take the loan from? Support your answer with calculations.

c. A contract requires you to make a payment of $2,500 immediately upfront and additional three payments of $500 each at the end of next three years. If interest rate on this investment is 8.5%, calculate the present value of the contract?

Answer 1

a)

number of periods in retirement = 15*12 = 180

Interest rate = 7%/12

[N = 180 ; I/Y = 7%/12 ; PV = ? ; PMT = 2400 ; FV = 0] Compute (CPT button) for PV

Present value = $267,014.30 (at t = 6)

Present value today (at t = 0)

number of periods = 6*6 = 36 periods

[N = 36 ; I/Y = 7%/12 ; PV = ? ; PMT = 0 ; FV = 267014.30]

so balance today = $216,569.68

b)

(we do not need calculator to solve this question)

We must calculate Effective annual rate (EAR) for both banks and compare them. we should choose the bank with Lower EAR

EAR = (1+(r/n))^n - 1

r = Nominal rate

n = number of compounding periods

Bank a:

EAR = (1 + (6%/4))^4 - 1 = 6.136%

Bank b:

EAR = (1 + (5.98%/365))^365 - 1 = 6.162%

Since EAR of Bank a is lower we should select Bank a

c)

Present value of 500 payments

[N = 3 ; I/Y = 8.5% ; PV = ? ; PMT = 500 ; FV = 0]

PV = 1277.01

Present value of contract = 1277.01 + 2500 = $3777.01