Question

1) Investment X for 100,000 is invested at a nominal rate of interest, j, convertible semi-annually. After four years, it accumulates to 214,358.88.

Investment Y for 100,000 is invested at a nominal rate of discount, k, convertible quarterly. After two years, it accumulates to 232,305.73.

Investment Z for 100,000 is invested at an annual effective rate of interest equal to j in year one and an annual effective rate of discount equal to k in year two.

Calculate the value of investment Z at the end of two years.

A. 168,000

B. 182,900

C. 184,425

D. 200,000

E. 201,675

2) You are given a perpetuity, with annual payments as follows:

1. Payments of 1 at the end of the first year and every three years thereafter.
2. Payments of 2 at the end of the second year and every three years thereafter.
3. Payments of 3 at the end of the third year and every three years thereafter.

The interest rate is 5% convertible semi-annually.

Calculate the present value of this perpetuity.

A. 24

B. 29

C. 34

D. 39

E. 47

3) A bank offers the following certificates of deposit:

The bank requires that interest accumulate at the certificate’s interest rate, and does not permit early withdrawal. The certificates mature at the end of the term. During the next six years, the bank will continue to offer these certificates of deposit.

Jeff invests 1000 in the bank.

Calculate the maximum amount he can withdraw at the end of six years.

A. 1480

B. 1510

C. 1540

D. 1570

E. 1600

Answer 1

1).

- Investment X = $100,000

After 4 years Amount will accumulated to (future value) = $214,358.88

As, the interest is compounded semiannually,

Future Value = Invested amount(1+r/2)^n*2

n = 4

214358.88 = 100000(1+r/2)^4*2

2.1435888 = (1+r/2)⁸

Taking 8 root on both sides,

1.0991 = (1+r/2)

0.10 = r/2

r = 20%

Effective Annual rate = [(1+r/2)²-1]

= [(1+0.20/2)²-1]

= 21%

- Investment Y = $100,000

After 4 years Amount will accumulated to (future value) = $232,305.73

As, the interest is compounded Quarterly,

Future Value = Invested amount(1+r/4)^n*4

n = 2

232,305.73 = 100000(1+r/4)^n*4

2.3230573 = (1+r/4)⁸

Taking 8 root on both sides,

1..1111 = (1+r/4)

0.1111 = r/4

r = 44.44%

Effective Annual rate = [(1+r/4)⁴-1]

= [(1+0.4444/4)⁴-1]

= 52.41%

- Investment amount in Z = $100,000

Effective interest rate of Investment X = 21%

Investment Z after 1 year = 100000(1+0.21)

= 121000

Effective interest rate of Investment Y = 52.41%

Investment Z after 1 year = 121000(1+0.5241)

= $184416.1

So, Ans is Option C. $184,425 (ans is marginally differenent because of decimal rounding off)

NOTE- As per Chegg guidelines, I'm only allowed to answer 1 question per answer. So, Ques- 1 is answered.

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