Question

 

a) You have an opportunity to invest in an investment plan for the next 45 years. This plan will offer compound interest of 8 percent per year for the next 20 years and 11 percent per year for the last 25 years. If you invest $8,000 in this plan today, how much will you accumulate at the end of the 45 years?

Choose the correct answer:

$505,539.84

$501,516.38

$506,570.12

$509,092.54

$592,394.59

b)

Your rich uncle will give you a gift of $6,000 at your graduation one year from now. You will invest this in an investment opportunity that promises to pay 8 percent, compounded annually, until you have $60,000. How long will you need to wait, counting from today, till you accumulate this amount?

Choose the correct answer:

32.08 years

30.92 years

24.55 years

37.57 years

29.92 years

c)

Your fixed deposit account will mature in two years from now and will pay $7,500 to you at that time. After receiving it, you will invest it in another investment at 4.5 percent per year. How much will this new investment be worth ten years from now?

Choose the correct answer:

$10,665.75

$9,110.24

$11,617.07

$10,113.33

$11,428.09

d)

“Bank A” pays 6 percent simple interest on its savings account balances, whereas “Bank B” pays 6 percent compounded annually. If you deposited $10,000 in Bank A and another $10,000 in Bank B, how much more money would you earn in Bank B as compared to your balance in Bank A, at the end of 5 years?

Choose the correct answer:

$340.09

$382.26

$450.75

$360.47

$350.14

Answer 1

Question a:

P = Initial investment = $8,000

n1 = 20 yeras

n2 = 25 years

r1 = interest rate = 8%

r2 = interest rate = 11%

Future Value = P * (1+r1)^n1 * (1+r)^n2

= $8,000 * (1+8%)^20 * (1+11%)^45

= $8,000 * 4.66095714 * 13.5854638

= $506,570.116

Therefore, accumulated value in 45 years is $506,570.12

Question b:

PV = Amount invested = $6,000

FV = Future Value = $60,000

r = interest rate = 8%

n = number of years

FV = PV * (1+r)^(n-1)

$60,000 = $6,000 * (1+8%)^(n-1)

(1.08)^(n-1) = 10

n-1 = log (10) / log(1.08)

n-1 = 1 / 0.0334237555

n-1 = 29.9188402

n = 30.9188402

Therefore, it will take 30.92 years to accumulate the amount

Question c:

PV = Amount received = $7,500

n = 10-2 = 8 years

r = interest rate = 4.5%

Future Value = PV * (1+r)^n

= $7,500 * (1+4.5%)^8

= $7,500 * 1.42210061

= $10,665.7546

Therefore, new investment worth in 10 years is $10,665.75

Question d:

P = Amount invested = $10,000

r = interest rate = 6%

t = 5 years

Bank A interest earned with simple interest = P * r * t

= $10,000 * 6% * 5

= $3,000

Bank B interet eaned with compounding interest = P * [(1+r)^n - 1]

= $10,000 * [(1+6%)^5 - 1]

= $10,000 * 0.33822558

= $3,382.2558

Difference in Interest earned = Bank B interet eaned with compounding interest - Bank A interest earned with simple interest

= $3,382.2558 - $3,000

= $382.2558

Therefore, the amount in Bank B will be higher than the amount in Bank A by $382.26