Question

1. What is the value of the following investments in the future? (show your work): a) b) c) d) e) $6,000 invested for 5 years at 16% compounded quarterly?.. $9,000 invested for 7 years at 8% compounded semi-annually? $875 invested for 1 year at 12% compounded monthly?» $22,000 invested for 5 years at 5% compounded annually?» How long will it take to double your investment if the interest rate is 3%?

Answer 1

a)

Number of periods = 5 * 4 = 20

Rate = 16% / 4 = 4%

Future value = Present value (1 + r)ⁿ

Future value = 6000 (1 + 0.04)²⁰

Future value = 6000 * 2.19112

Future value = $13,146.74

You can also find this using a financial calculator:

PV 6000

I/Y 4

N 20

CPT FV

b)

Number of periods = 7 * 2 = 14

Rate = 8% / 2 = 4%

Future value = Present value (1 + r)ⁿ

Future value = 9000 (1 + 0.04)¹⁴

Future value = 9000 * 1.73168

Future value = $15,585.09

You can also find this using a financial calculator:

PV 9000

I/Y 4

N 14

CPT FV

c)

Number of periods = 1 * 12 = 12

Rate = 12% / 12 = 1%

Future value = Present value (1 + r)ⁿ

Future value = 875 (1 + 0.01)¹²

Future value = 875 * 1.12683

Future value = $985.97

You can also find this using a financial calculator:

PV 875

I/Y 1

N 12

CPT FV

d)

Future value = Present value (1 + r)ⁿ

Future value = 22,000 (1 + 0.05)⁵

Future value = 22,000 * 1.27628

Future value = $28,078.19

You can also find this using a financial calculator:

PV 22,000

I/Y 5

N 5

CPT FV

e)

Let present value be $1

Future value be $2

Future value = Present value (1 + r)ⁿ

2 = 1 (1 + 0.03)ⁿ

LN 2 = n LN 1.03

0.69315 = n 0.02956

n = 23.45

It will take 23.45 years

You can also find this using a financial calculator:

PV -1

FV 2

I/Y 3

CPT N