Question

ECONOMIC DECISION MAKING

PLEASE TYPE OUT ALL THE RESPONSES

1. How much will accumulate in an account at the end of 10 years if $5,000 is deposited today and the account earns 4% interest, annually? What if compounded quarterly? What if compounded monthly?
2. If you were looking to replace your roof in three years, at an expected cost of $8,500, how much would you have to set aside in equal annual amounts, if you can earn 6% interest?
3. Suppose you deposit $65,000 in an account today that pays 5% interest, compounded annually. How much will you have in the account in 25 years?
4. You acquire a new truck for your business. The cost of the vehicle is $42,500. You are provided financing for five years at an interest rate of 6%. What are the monthly payments?
5. Complete the following solving for the Future Value:
   1. Present Value $35,000, Interest Rate 8% and N=9
   2. Present Value $539,400, Interest Rate 6.5% and N=36 Months
   3. Present Value $3,000, Interest Rate 5% and N=3

Answer 1

Annual Interest:

FV After 10 years = 5000*(1+4/100)^10 = 7401.22

Compounded quarterly

FV After 10 years or 40 quarters = 5000* (1+4/400)^40 = 7444.32

Compounded Monthly

FV after 10 years or 120 months = 5000 * (1+4/1200)^120 = 7454.16

Let the equal installment amount be x and the amount is deposited at the beginning of every year

So x*1.06^3 + x * 1.06^2 + x*1.06^1 = 8500

or x*(1.19016 + 1.1236 + 1.06) = 8500

or x = 8500 / 3.37376

or x = 2519.44

So an amount of 2519.44 needs to be deposited at the beginning of every month to get the roof after 3 years.

Amount after 25 years = 65000 * (1+5/100)^25 = 220113.07

Let the monthly payments be x

So 42500 = x/(1+6/1200)^1 + x/(1+6/1200)^2 + x/(1+6/1200)^3+...+ + x/(1+6/1200)^60

or 42500 = x/(1+6/1200) * (1/(1+6/1200)^60 - 1) / (1/(1+6/1200) - 1)

or 42500 = x / 1.005 * 0.2586 / 0.004975

or x = 42500 * 1.005 * 0.004975 / 0.2586

or x = 821.71

So an equated monthly payment of 821.71 is needed.

1. Present Value $35,000, Interest Rate 8% and N=9. FV = 35000 * (1+8/100)^9 = 69965.16
2. Present Value $539,400, Interest Rate 6.5% and N=36 Months. FV = 539400 * (1+6.5/1200)^36 = 655193.88
3. Present Value $3,000, Interest Rate 5% and N=3 FV = 3000 * (1+5/100)^3 = 3472.88

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