bmaggie

An investor wants to receive $1,000 at the beginning of each of the next ten years with the first payment starting today. If the investor can earn 10 percent interest, what must the investor put into the account today in order to receive this $1,000 cash flow stream?

A) $6,145.

B) $6,759.

C) $7,145.

---

This is an annuity due problem. There are several ways to solve this problem.

Method 1:

PV of first $1,000 = $1,000
PV of next 9 payments at 10% = 5,759.02
Sum of payments = $6,759.02

Method 2:

Put calculator in BGN mode.
N = 10; I = 10; PMT = -1,000; CPT → PV = 6,759.02
Note: make PMT negative to get a positive PV. Don’t forget to take your calculator out of BGN mode.

Method 3:

You can also find the present value of the ordinary annuity $6,144.57 and multiply by 1 + k to add one year of interest to each cash flow. $6,144.57 × 1.1 = $6,759.02.

bmaggie

An investor purchases a 10-year, $1,000 par value bond that pays annual coupons of $100. If the market rate of interest is 12%, what is the current market value of the bond?

A) $887.

B) $1,124.

C) $950.

---

Note that bond problems are just mixed annuity problems. You can solve bond problems directly with your financial calculator using all five of the main TVM keys at once. For bond-types of problems the bond’s price (PV) will be negative, while the coupon payment (PMT) and par value (FV) will be positive. N = 10; I/Y = 12; FV = 1,000; PMT = 100; CPT → PV = –886.99.

bmaggie

An investor will receive an annuity of $5,000 a year for seven years. The first payment is to be received 5 years from today. If the annual interest rate is 11.5%, what is the present value of the annuity?

A) $15,000.

B) $13,453.

C) $23,185.

---

With PMT = 5,000; N = 7; I/Y = 11.5; value (at t = 4) = 23,185.175. Therefore, PV (at t = 0) = 23,185.175 / (1.115)⁴ = $15,000.68.

bmaggie

If $2,500 were put into an account at the end of each of the next 10 years earning 15% annual interest, how much would be in the account at the end of ten years?

A) $41,965.

B) $50,759.

C) $27,461.

---

N = 10; I = 15; PMT = 2,500; CPT → FV = $50,759.

bmaggie

Concerning an ordinary annuity and an annuity due with the same payments and positive interest rate, which of the following statements is most accurate?

A) The present value of the ordinary annuity is greater than an annuity due.

B) There is no relationship.

C) The present value of the ordinary annuity is less than an annuity due.

---

With a positive interest rate, the present value of an ordinary annuity is less than the present value of an annuity due. The first cash flow in an annuity due is at the beginning of the period, while in an ordinary annuity, the first cash flow occurs at the end of the period. Therefore, each cash flow of the ordinary annuity is discounted one period more.

bmaggie

How much would the following income stream be worth assuming a 12% discount rate?

• $100 received today.
• $200 received 1 year from today.
• $400 received 2 years from today.
• $300 received 3 years from today.

A) $721.32.

B) $810.98.

C) $1,112.44.

---

N	i	FV	PV
0	12	100	100.00
1	12	200	178.57
2	12	400	318.88
3	12	300	213.53
			810.98

bmaggie

You borrow $15,000 to buy a car. The loan is to be paid off in monthly payments over 5 years at 12% annual interest. What is the amount of each payment?

A) $546.

B) $456.

C) $334.

---

I = 12 / 12 = 1; N = 5 × 12 = 60; PV = 15,000; CPT → PMT = 333.67.

bmaggie

An investor deposits $4,000 in an account that pays 7.5%, compounded annually. How much will this investment be worth after 12 years?

A) $5,850.

B) $9,358.

C) $9,527.

---

N = 12; I/Y = 7.5; PV = -4,000; PMT = 0; CPT → FV = $9,527.

bmaggie

An annuity will pay eight annual payments of $100, with the first payment to be received one year from now. If the interest rate is 12% per year, what is the present value of this annuity?

A) $1,229.97.

B) $556.38.

C) $496.76.

---

N = 8; I/Y = 12%; PMT = -$100; FV = 0; CPT → PV = $496.76.

bmaggie

Renee Fisher invests $2,000 each year, starting one year from now, in a retirement account. If the investments earn 8% or 10% annually over 30 years, the amount Fisher will accumulate is closest to:

                     8%                     10%

A) $225,000 $360,000

B) $225,000 $330,000

C) $245,000 $360,000

---

N = 30; I/Y = 8; PMT = -2,000; PV = 0; CPT FV = 226,566.42

N = 30; I/Y = 10; PMT = -2,000; PV = 0; CPT FV = 328,988.05