Question

QUESTION 1

a) Calculate the future sum of $5,000, given that it will be held in a bank 5 years at an annual interest rate of 6% compounded annually.

b) Recalculate part (a) using SIMPLE INTEREST. What would be the amount of interest received?

c) Recalculate part (a) using compounding periods that are i) semiannual and ii) quarterly

d) Recalculate part (a) and (b) for a 12% annual interest rate.

e) Recalculate part (a) using a time horizon of 12 years (annual interest rate is still 6%).

f) With respect to the effect of changes in the interest rate and holding periods on future sums

(that is your answer) in part (c) and (d), what conclusions do you make when you compare these figures with the answers found in part (a) and (b)?

QUESTION 2

A magazine publisher offers its customers three option on subscriptions:

Option A: $50 today for three years.

Option B: A two-year rate of $38 paid immediately, followed by a one-year rate of $17 paid

at the beginning of the third year.

Option C: $17 paid at the beginning of each of the three years.

a) From the perspective of the company, which option is best if the company’s opportunity cost of funds is 8%? Explain.

b) From the perspective of the subscriber, which option is best in terms of minimizing the cost of subscription if the subscriber’s opportunity cost of funds is 5%? Explain.

QUESTION 3

Bart Simpson, now age 10, wants to be able to buy a really cool new car when he turns 16. His really cool car costs $15,000 today, and its cost is expected to increase 3% annually. Bart wants to make one deposit today (he can sell his original collection of The Spiderman comic books) into an account paying 8% annually in order to buy his dream car. How much will Bart’s car cost? And how much does Bart have to save today in order to buy this car at age 16?

QUESTION 4

Lisa Simpson is planning to attend college when she graduates from high school 7 years from now. She anticipates that she will need an amount of $35,770.97 for her 4-year college to pay for tuition and fees, and have some spending money. Lisa has made an arrangement with her father to do the household chores if her dad deposits $3,500 at the end of each year for the next 7 years in a bank account paying 8 percent interest. Will there be enough money in the account for Lisa to pay for her college expenses?

Answer 1

Question 1

a]

future value = present value * (1 + r)ⁿ,

where r = periodic rate of interest

n = number of periods.

Here, r = annual rate, which is 6%; and n = number of years = 5

future value = $5,000 * (1 + 6%)⁵ = $6,691.13

b]

Total simple interest received = invested amount * interest rate * number of years

Total simple interest received = $5,000 * 6% * 5 = $1,500

Future value = invested amount + total interest = $5,000 + $1,500 = $6,500

c]

i]

future value = present value * (1 + r)ⁿ,

where r = periodic rate of interest

n = number of periods.

Here, r = semiannual rate, which is 6%/2 = 3%; and n = number of semiannual periods = 5 * 2 = 10.

future value = $5,000 * (1 + 3%)¹⁰ = $6,719.58

ii]

future value = present value * (1 + r)ⁿ,

where r = periodic rate of interest

n = number of periods.

Here, r = quarterly rate, which is 6%/4 = 1.5%; and n = number of quarters = 5 * 4 = 20.

future value = $5,000 * (1 + 1.5%)²⁰ = $6,734.28

d]

compound interest

future value = present value * (1 + r)ⁿ,

where r = periodic rate of interest

n = number of periods.

Here, r = annual rate, which is 12%; and n = number of years = 5

future value = $5,000 * (1 + 12%)⁵ = $8,811.71

simple interest

Total simple interest received = invested amount * interest rate * number of years

Total simple interest received = $5,000 * 12% * 5 = $3,000

Future value = invested amount + total interest = $5,000 + $3,000 = $8,000