Question

7. Consider Donald and Joe who are both 30- years of age and recently graduated with a degree in Finance. Both Donald and Joe plan to retire at age 67, and the retirement plan pays a 12 percent per annum return and is also compounded monthly. Donald plans to invest $1,000 per month beginning next month into his retirement account, while Joe shall invest $2,000 per month. Joe however does not plan to begin investing until 10 years after Donald begins to invest. How much will each of the newly grads have at retirement?

8. On December 31, 2019, Speedo’s Limited bought a yacht for $55,000 but made a down payment of $10,000. Speedo’s agreed to pay the balance in 10 equal end-of-year installments and 10% interest on the declining balance. Calculate the annual payments.

9. Match each sentence to the correct concept.

a) The amount an investment is worth after one or more time periods is referred to as _______________

b) The process of finding the present value of some future amount is called _________________.

c) Calculating the present value of a future cash flow to determine its value today is known as _________________.

d) Interest earned on the principal and may be for a number of years may be called ______________

e) ___________ is the process of accumulating interest in an investment over time to earn more interest.

f) The interest earned on both the initial principal and the interest reinvested from prior periods is referred to as ______ _______.

Answer 1

7]

Donald

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. This is $1,000

r = periodic rate of interest. This is (12%/12) = 1%, or 0.01. We divide by 12 since we need to convert the annual rate into monthly rate)

n = number of periods. This is 37 * 12 = 444 (there are 37 years, or 444 months in the investment period)

Future value of annuity = $1,000 * [(1 + 0.01)⁴⁴⁴ - 1] / 0.01

Future value of annuity = $8,192,585.53

Donald will have $8,192,585.53 at retirement

Joe

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. This is $2,000

r = periodic rate of interest. This is (12%/12) = 1%, or 0.01. We divide by 12 since we need to convert the annual rate into monthly rate)

n = number of periods. This is 27 * 12 = 324 (there are 27 years, or 324 months in the investment period)

Future value of annuity = $2,000 * [(1 + 0.01)³²⁴ - 1] / 0.01

Future value of annuity = $4,825,220.25

Joe will have $4,825,220.25 at retirement