Question

Cla: Checked Annuities (PV and FV) Annual Amount Deposited 950 Annual Interest Rate Deposits are made for each of years 1 - 40. 9.5% 1. Future value of ordinary annuity. What will these deposits have grown to by end of year 40? A Between 50.000 and 212,000 B Between 212.000 and 253.000 C Between 253,000 and 312,000 D Between 312.000 and 420,000 2. Future value of annuity due What will these deposits have grown to by end of year 402 A Between 50,000 and 227.000 B Between 227.000 and 269,000 C Between 269.000 and 329,000 D Between 329.000 and 420.000 3. Present value of ordinary annuity What are these deposits worth today? A Between 5.000 and 9,400 B Between 9.400 and 10,300 C Between 10.300 and 11.200 D Between 11.200 and 15.000 4. Present value of annuity due What are these deposits worth today? A Between 5,000 and 10,100 B Between 10.100 and 11.100 C Between 11,100 and 12,100 D Between 12,100 and 15,000

Answer 1

1. Calculating the Future Value of Annuities using the Future value of Ordinary Annuity Formula:

|(1+r)" - 11 FutureValue = C*

Where, C= Periodic Payments = $950

r = Periodic Interest rate = 0.095

n= no of periods = 40

[(1 + 0.095)40 - 11 FutureValue = 950 * 0.095

FutureValue = 950 (37.719399 - 11 0.095

Future Value = $ 367193.99

So, Answer is Option D

2. Calculating the Future Value of Annuities using the Future value of Annuity Due Formula:

FutureValue = C+ ((1+r)" – 1].. 1*(1+

Where, C= Periodic Payments = $950

r = Periodic Interest rate = 0.095

n= no of periods = 40

|(1 + 0.095) FutureValue = 950 * -1] *(1+0.095) 0.095

|(37.719399 - 11 FutureValue = 950 * 1 1*(1 +0.095) 0,095

Future Value = $ 402,077.42

So, Answer is Option D

3. Calculating the Present  Value of Annuities using the Present value of Ordinary Annuity Formula:

PresentValue = C* [1 – (1 + r)-ny

Where, C= Periodic Payments = $950

r = Periodic Interest rate = 0.095

n= no of periods = 40

PresentValue = 950 * 1 0 [1 - (1 + 0.095) -40 0.095

PresentValue = 950 * 1 [1 – 0.0265116] 1.095

Present Value = $ 9734.88

So, Answer is Option B

4. Calculating the Present  Value of Annuities using the Present value of Annuity Due Formula:

[1 – (1 + r) -"] PresentValue = C* 5*(1+r)

Where, C= Periodic Payments = $950

r = Periodic Interest rate = 0.095

n= no of periods = 40

PresentValue = 950 * 1 [1 - (1 + 0.095) -40 5*(1 + 0.095) 0.095

1 -0.0265116 PresentValue = 950 * 1 T*(1 + 0.095) 0,095

Present Value = $ 10659.70

So, Answer is Option B

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