Question

1. Allright Corporation started making sinking fund deposits of $20,000 today. Its bank pays 5% compounded semi-annually and the deposits will be made at the beginning of every six months for 20 years. What will the fund be worth at the end of that time?

a. $1,381,752

b. $1,567,980

c. $1,425,658

d. $1,623,876

2. Given a 30-year mortgage loan of $100,000, monthly pay in arrrears, fully amortizing with an annual interest rate of 5%, what is the balance of the loan after the 60th payment?

a. $90,238.12

b. $91,828.73

c. $91,543.28

d. $91,776.99

3. The bank has extended a fully amortizing $500,000 monthly pay in arrears 15-year mortgage at 4%. What is the cumulative amount of interest and cumulative amount of principal for the periods 13 to 24?

a.$18,536.26; $25,845.02

b.$19,127.54; $25,253.74

c. $18,226.98; $ 26,154.30

d. $19,511.78; $24,869.50

Answer 1

Problem 1 –

The correct option is a. $1,381,752

This problem is related to Annuity due where the deposit or payment is made at the beginning of period for a specified period of time. The deposit or payment amount is same.

The fund worth at the end of time = Deposit amount x Present Annuity due factor at R rate for n period (Refer note below)

= $20,000 * 69.08762

= $1,381,752

Semi Annual rate of interest = 5% / 2 = 2.5% or 0.025

Semi Annual Period to maturity = 20 * 2 = 40

Present Value factor for Annuity Due = (1+R) x ((1 + R)n – 1) / R

= (1+0.025) x ((1+0.025)40 – 1) / 0.025

= 69.08762

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