Question 1

You deposit $100 in a bank for a fixed 7 year term. Interest on the deposit is calculated every half-year (m = 2)at the rate of 5% per half-year (i/m = 5%). Because the term is fixed, you are not allowed to withdraw interest at any point. You earn interest in the final compounding period of the term. How much of that interest is earned off of earlier interest (as opposed to earned off of the principal)?

Accepted Answer

Step 1 - Calculate the future value at the end of the period.
FV = PV × 11ea7fdb_fc28_d06f_a768_f793be4004f1_TB2902_00 FV = 100 × (1.05 11ea7fdb_fc28_f780_a768_1d1fd5a4a797_TB2902_00 = $188.56
Using a financial calculator:
N = 13, I/Y = 5, PV = -100, PMT = 0, cpt FV = $188.56
Step 2 - Find how much interest has been earned.
188.56 - 100 = $88.56
Step 3 - Calculate how much interest will be earned off of that interest.
88.56 × .05 = $4.428 or $4.43

Question 2

How long does it take for your money to double when invested at the rate of 3% (with annual compounding)?

Accepted Answer

Using a financial calculator:
I/Y = 3%, PV = -1, PMT = 0, FV = 2, cpt N = 23.45 or 24 years

Question 3

You invest $2,500 today at an interest rate of 20% compounded annually. How much will you accumulate after 35 years?

Accepted Answer

FV = PV × 11ea7fdb_fc28_8248_a768_9f322e6fb79b_TB2902_00 FV = 2,500 × 11ea7fdb_fc28_8249_a768_bd92cc8b2dd6_TB2902_00 = $1,476,670.57
Using a financial calculator:
N = 35, I/Y = 20, PV = -2,500, PMT = 0, cpt FV = $1,476,670.57

Question 4

You currently have $48,000 in your bank account, which pays annual interest of 5%, and you are saving up to buy a brand new $150,000 Jaguar convertible. In how many years will you have enough money to buy the car?

Accepted Answer

Using a financial calculator:
I/Y = 5%, PV = -48,000, PMT = 0, FV = 150,000, cpt N = 23.35 or 24 years

Question 5

Shylock Bank offers a savings account with an effective interest rate of 9% and quarterly compounding. What is the nominal rate (APR)on the account?

Accepted Answer

Effective interest rate = 11ea7fdb_fc29_1e95_a768_f7290a4abe64_TB2902_00 - 1
.09 = 11ea7fdb_fc29_45a6_a768_ef14936c37d5_TB2902_00 - 1
1.09 = 11ea7fdb_fc29_45a7_a768_f1a6638c7ade_TB2902_00 1.02177 = 11ea7fdb_fc29_45a8_a768_fb54f00c0951_TB2902_00 .02177 = 11ea7fdb_fc29_45a9_a768_07a77a5ba991_TB2902_00 i = 8.71%

Question 6

Shylock Bank offers a savings account with an effective interest rate of 15% and weekly compounding. What is the nominal rate (APR)on the account?

Accepted Answer

Effective interest rate = 11ea7fdb_fc29_6cba_a768_eff31f3650da_TB2902_00 - 1
.15 = 11ea7fdb_fc29_6cbb_a768_17644c69a4ba_TB2902_00 - 1
1.15 = 11ea7fdb_fc29_6cbc_a768_71ab452c1022_TB2902_00 1.00269 = 11ea7fdb_fc29_6cbd_a768_7719d6fac8cf_TB2902_00 .00269 = 11ea7fdb_fc29_6cbe_a768_85f8a097b331_TB2902_00 i = 14%

Question 7

Your Godmother established a $3,000 bank account for you when you were born. For the first 10 years the interest rate on the account was 10%. It has been 7.5% since then. You are now 25 years old and would like to withdraw the funds. How much money do you have?

Accepted Answer

FV = PV × 11ea7fdb_fc27_e5fd_a768_4b702eeed0d8_TB2902_00 FV = 3,000 × 11ea7fdb_fc27_e5fe_a768_05f825655965_TB2902_00 × 11ea7fdb_fc28_0d0f_a768_7bcea157e519_TB2902_00 = $23,023.70 Using a financial calculator: N = 10, I/Y = 10, PV = -3,000, PMT = 0, cpt FV = $7,781.23 N = 15, I/Y = 7.5, PV = -7,781.23, PMT = 0, cpt FV = $23,023.70

Question 8

Shylock Bank offers a savings account with a nominal rate of 7% and daily compounding. What is the effective rate of the account? (Assume a 365 day year.)

Accepted Answer

Effective interest rate = 11ea7fdb_fc28_f781_a768_b72733f388b7_TB2902_00 - 1
Effective interest rate = 11ea7fdb_fc28_f782_a768_7d1e0ee12d63_TB2902_00 - 1 = 7.25%

Question 9

In order to open up your new business you need to take out a loan. First Bank charges 6% compounded quarterly, and Second Bank charges 6.5% compounded semi-annually. From which bank would you prefer to obtain your loan?

Accepted Answer

Effective interest rate = 11ea7fdb_fc29_93cf_a768_b14726ff263f_TB2902_00 - 1
Effective interest rate for First Bank = 11ea7fdb_fc29_93d0_a768_73beef6173d5_TB2902_00 - 1 = 6.14%
Effective interest rate for Second Bank = 11ea7fdb_fc29_93d1_a768_c1dce523ed5c_TB2902_00 - 1 = 6.61%

Question 10

You wish to deposit $7,000 in an account at the Shylock Bank. The bank pays interest at a nominal annual rate of 10% compounded quarterly. What is the effective interest rate offered by Shylock?

Accepted Answer

Effective interest rate = 11ea7fdb_fc29_e1f7_a768_b99bc9b28397_TB2902_00 - 1
Effective interest rate = 11ea7fdb_fc29_e1f8_a768_fb91e9bcc86e_TB2902_00 - 1 = 10.38%

Question 11

Leon's has a "Don't Pay For One Year" event on right now at the store, so you purchase an Italian, hand-stitched leather sofa. You will pay $1,267.99 for the sofa in one year. Leon's charges 18% annual interest compounded monthly on overdue payments. If you forget and don't pay for the sofa until 6 months after payment is due, how much will you pay for the sofa at that time?

Accepted Answer

FV = PV × 11ea7fdb_fc29_bae5_a768_11925ecb9067_TB2902_00 FV = 1,267.99 × (1.015 11ea7fdb_fc29_e1f6_a768_b7e486b8cc80_TB2902_00 = $1,386.48
Using a financial calculator:
N = 6, I/Y = 1.5, PV = -1,267.99, PMT = 0, cpt FV = $1,386.48

Question 12

Jordan will need $20,000 at the end of 6 years to put a down payment on a house. What rate of return will he need to earn if he can invest $12,250 today?

Accepted Answer

i = 11ea7fdb_fc28_3424_a768_ed12f257eb7c_TB2902_00 - 1
i = 11ea7fdb_fc28_5b35_a768_0dcb1771cce6_TB2902_00 - 1 = 8.5%
Using a financial calculator:
N = 6, PV = -12,250, PMT = 0, FV = 20,000, cpt I/Y = 8.5%

Question 13

Henry purchased stock in Nortel Networks for $120 per share. Unfortunately the stock did not perform very well in the 3 years that Henry has owned it as it is now trading at $3.93 per share. Feeling that the value of the stock will only continue to drop, Henry sold his shares today. What annual rate of return did Henry make on his investment?

Accepted Answer

i = 11ea7fdb_fc28_3422_a768_d3eaee2b47ee_TB2902_00 - 1
i = 11ea7fdb_fc28_3423_a768_1509f3a459ac_TB2902_00 - 1 = -68%
Using a financial calculator:
N = 3, PV = -120, PMT = 0, FV = 3.93, cpt I/Y = -68%

Question 14

Jordan will need $20,000 at the end of 6 years to put a down payment on a house. What rate of return will he need to earn if he can invest $9,110 today?

Accepted Answer

i = 11ea7fdb_fc28_5b36_a768_b9efe52b0142_TB2902_00 - 1
i = 11ea7fdb_fc28_5b37_a768_3dc4e02c4fde_TB2902_00 - 1 = 14%
Using a financial calculator:
N = 6, PV = -9,110, PMT = 0, FV = 20,000, cpt I/Y = 14%

Question 15

If you could borrow at 9.5% compounded semi-annually or at 9.4% compounded monthly, which would you prefer?

Accepted Answer

Effective interest rate = 11ea7fdb_fc29_bae2_a768_0943ffd62860_TB2902_00 - 1
Effective interest rate for semi-annual = 11ea7fdb_fc29_bae3_a768_b5c146f007fc_TB2902_00 - 1 = 9.73%
Effective interest rate for monthly = 11ea7fdb_fc29_bae4_a768_494b742b6093_TB2902_00 - 1 = 9.82%

Question 16

You have come across an investment opportunity that will give you $51,725.29 in 14 years if you put up $12,000 today. Calculate the annual return on this investment.

Accepted Answer

i = 11ea7fdb_fc28_0d10_a768_238e2eed64f3_TB2902_00 - 1
i = 11ea7fdb_fc28_0d11_a768_27df8af5bd86_TB2902_00 - 1 = 11%
Using a financial calculator:
N = 14, PV = -12,000, PMT = 0, FV = 51,725.29, cpt I/Y = 10.999 or 11%

Question 17

You put $100 in a bank for a fixed two year term. The interest rate on the loan is 8% per annum, compounded semi-annually. Because the term is fixed, you are not allowed to withdraw interest at any point. What is the total amount of interest earned in the final half-year of the term?

Accepted Answer

Step 1 - Calculate the future value of the last two periods.
FV = PV × 11ea7fdb_fc28_a95c_a768_13b606dbc1ab_TB2902_00 FV = 100 × (1.04 11ea7fdb_fc28_d06d_a768_0705771805a9_TB2902_00 = $116.99
Using a financial calculator:
N = 4, I/Y = 4, PV = -100, PMT = 0, cpt FV = $116.99
FV = 100 × (1.04 11ea7fdb_fc28_d06e_a768_4f044b9354c8_TB2902_00 = $112.49
Using a financial calculator:
N = 3, I/Y = 4, PV = -100, PMT = 0, cpt FV = $112.49
Step 2 - Take the difference between the future values to find how much interest was earned in the last period.
116.99 - 112.49 = $4.50

Question 18

You have $602.42 today. You want to accumulate $1,320 by investing your money. You have identified an investment that will generate a return of 4% per annum. How long will you have to invest (in years)in order to accumulate your desired total?

Accepted Answer

Using a financial calculator:
I/Y = 4%, PV = -602.42, PMT = 0, FV = 1,320, cpt N = 20 years

Question 19

Shylock Bank offers a savings account with a nominal rate of 9% and quarterly compounding. What is the effective rate of the account?

Accepted Answer

The effective rate formula for quarterly compounding is (1 + (nominal rate/4))^4 - 1. Substituting the given values, we get (1+(0.09/4))^4 - 1 = 0.0931 or 9.31%. Therefore, the effective rate of the account is 9.31%.

Question 20

You have $253.05 today. A friend wants to borrow that money from you and pay you back $310 at the end of 3 years. What rate of return (per annum)will you earn from the loan?

Accepted Answer

i = 11ea7fdb_fc28_a95a_a768_87425f9c6cbf_TB2902_00 - 1
i = 11ea7fdb_fc28_a95b_a768_f96ea8285efb_TB2902_00 - 1 = 7%
Using a financial calculator:
N = 3, PV = -253.05, PMT = 0, FV = 310, cpt I/Y = 7%

Quiz 3: Time Value of Money - Introduction

How long does it take for your money to double when invested at the rate of 3% (with annual compounding) ?