Question

11. An investor places $5,000 in an account. The stated annual interest rate is 6% compounded monthly. The value of the account at the end of three years is closest to: *

A. $5,970.

B. $5,978.

C. $5,983.

D. $5,980.

E. None of the above.

12. If an investment of $4,000 will grow to $6,250 in four years with monthly compounding, the annual interest rate will be closest to: *

A. 11.2%.

B. 12.3%.

C. 13.0%.

D. 14.0%.

E. None of the above.

13. Frank Jones is considering three separate investments. Investment 1 pays a stated annual interest rate of 6.1%, compounded annually. Investment 2 pays a stated annual interest rate of 6.0%, compounded monthly. Investment 3 pays a stated annual interest rate of 5.9%, compounded quarterly. Which investment should smith choose? *

A. Investment 1.

B. Investment 2.

C. Investment 3.

D. Indifferent between the three investments.

E. None of the above.

14. You have a saving account in the bank that pays you a rate of 8% compounded annually. If you deposit $750 at the end of the first year, $1,000 at the end of the second year, and $2,000 at the end of the fourth year, what will be the ending balance of your account at the end of the fourth year? *

A. $3,750.00

B. $4,111.18

C. $41,118.11

D. Cannot be determined.

E. None of the above.

15. You have a chance to buy an annuity that pays $20,000 at the beginning of each year for 6 years. You could earn 5% on your money in other investments with equal risk. What is the most value in the present you should pay for the annuity? *

A. $106,589.53

B. $120,000.00

C. $126,000.00

D. $162,000.00

E. None of the above.

Answer 1

11)FV=PV(1+r)^T

FV=Future value

PV=present value

R=Interest rate

T=Term

Here interest rate is 6%/annum,Hence for month it will be 6/12 or 0.5%

Term=12months*3=36 months

FV=5,000(1+0.005)^12=5983.403

12)Here FV=6,250

Currently you have 4,000 which is PV

Term is 48 months

Apply the above formula

6,250=4,000(1+r)^48

(1+r)^48=6,250/4,000

(1+r)^48=1.5625

48 th root of 1.5625=1+r(root value you can find out in scientific calculator or in internet)

1+r=1.009341

R=0.009341

Interest rate=0.9341/month

OR

11.20% per year

13)Lets take effective interest rate for each option

Effective interest rate=((1+r/t)^t)-1

Annual compounding

Effective interest rate=6.1%

Monthly compounding

Effective interest rate=((1+0.06/12)^12)-1=0.61678or 6.1678%

Quarterly compounding

Effective interest rate=((1+0.059/4)^4)-1=0.060318

Or 6.0318%

Hence it is proved that monthly compounding with 6% annual interest rate is better(Investment 2)

14)

FV=PV(1+r)^t

Since deposit is made in the end of the year term will be 1 year less.

For last year there will be no interest accrued since deposit made in the year end

YEAR	DEPOSIT	INTEREST Computation	Interest	TOTAL
1	750	750(1+0.08)^3	944.784	1694.784
2	1000	1000(1+0.08)^2	1166.4	2166.4
3	-	-	-	0
4	2000	-	-	2000
TOTAL	5861.184

So answer is none of the above

15)Present value of annuity

YEAR	Annuity	PVF @5%	DCF
0	20,000	1/(1.05)^0=1	20000
1	20,000	1/(1.05)^1=0.9524	19047.619
2	20,000	1/(1.05)^2=0.9070	18140.5896
3	20,000	1/(1.05)^3=0.8638	17276.752
4	20,000	1/(1.05)^4=0.8227	16454.0495
5	20,000	1/(1.05)^5=0.7835	15670.5233
TOTAL	106589.533

Currently we can pay 106589 for bond.

Since Annuity is paid in the beginning of the year we have taken 0 as 1 st year beginning and 5 as 6 th year beginning to obtain the correct present value.