1. How many years will it take $400 to grow to $1671 if it is invested at 10 per

Question

1. How many years will it take $400 to grow to $1671 if it is invested at 10 percent compounded annually?

2. At what rate would $1000 have to be invested to grow to $4046 in 10 years ?

3. What is the present value of an ordinary annuity of $1000 per year for 7 years discounted back to the present at 10 percent? What would be the present value if it were an annuity due?

4. You have just borrowed $100,000 and you agree to pay it back over the next 25 years in 25 equal end of the year payments plus 10 percent compound interest on the unpaid balance ? What will be the size of these payments?

5. What is the present value of a $1000 perpetuity discounted back to the present at 8 percent?

6. What is the present value of a $1000 annuity for 10 years, with the first payment occuring at the end of year 10( that is, ten $1000 payments occuring at the end of year 10 through year 19)given a discount rate of 10 percent?

7. Given a 10 percent discount rate, what is the present value of a perpetuity of $1000 per year if the first payment does not begin until the end of year 10?

Explanation / Answer

1)

1671 = 400 * (1+0.1)^t

t = 15 years

2)

4046 = 1000 * (1+r)^10

r = 15%

3)

PV = 1000 * [1- (1+0.1)^-7]/0.1 = 4868.42

PV of annuity due = 1000 * [1- (1+0.1)^-7]/0.1 * (1+0.1) = 5355.26

4)

let x be the anuula payments

x * [1 -(1.1)^-25]/0.1 = 100000

x = 11016.81

5)

PV = 1000/0.08 = 12500

6)

PV of annuity at year 9 = 1000 * [1-(1.1)^-10]/0.1 = 6144.567106

PV of annuity now = 6144.567106/1.1^9 = 2605.90

7)

PV at year 9 = 1000/0.1 = 10000

PV now = 10000/1.1^9 = 4240.98

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