Question

You just won $80,000 on a scratch-off lottery ticket. You plan to save the money in a retirement account expected to return 9% per year. If you intend to retire in 45 years, how much are these lottery winnings expected to be worth when you retire? $3,866,183 $871,576 $1,238,815 $9,665,457 $1,260,147 If you find an account that pays 10% annual interest instead of 9%, how much would you have at retirement? $1,890,221 $1,915,227 $3,250,123 $5,831,239 $14,578,097 Suppose the new retirement account actually pays 10% interest per year and pays interest monthly. How much money would you have at retirement? $2,043,797 $2,119,250 $1,105,609 $7,068,334 $17,034,358

Answer 1

1. Option (a) is correct

Here we will use the following formula:

FV = PV * (1 + r%)n

where, FV = Future value, PV = Present value = $80000, r = rate of interest = 9%, n= time period = 45

now, putting theses values in the above equation, we get,

FV = $80000 * (1 + 9%)45

FV = $80000 * (1 + 0.09)45

FV = $80000 * (1.09)45

FV = $80000 * 48.3272861046

FV = $3866183

So, the amount will be worth $3866183.

2. Option (d) is correct

Here we will use the following formula:

FV = PV * (1 + r%)n

where, FV = Future value, PV = Present value = $80000, r = rate of interest = 10%, n= time period = 45

now, putting theses values in the above equation, we get,

FV = $80000 * (1 + 10%)45

FV = $80000 * (1 + 0.10)45

FV = $80000 * (1.10)45

FV = $80000 * 72.8904836851

FV = $5831239

So, the amount will be worth $5831239.

3. Option (d) is correct

Here we will use the following formula:

FV = PV * (1 + r%)n

where, FV = Future value, PV = Present value = $80000, r = rate of interest = 10% compounded monthly, so monthly rate = 10% / 12 = 0.8333%, n= time period = 45 * 12 = 540 months

now, putting theses values in the above equation, we get,

FV = $80000 * (1 + 0.8333%)540

FV = $80000 * (1 + 0.008333)540

FV = $80000 * (1.008333)540

FV = $80000 * 88.3541809243

FV = $7068334

So, the amount will be worth $7068334.

Answer 2

SOLUTION :

1.

If interest rate is 9% and retire in 45 years :

r = 9% = 0.09

=> 1 + r = 1.09

A = 80000 ($)

n = 45

FV = A(1 + r)^n = 80000*1.09^45 = 3866183 ($) : First Option (ANSWER)

2.

If interest rate is 10 % inlace of 9% :

r = 10% = 0.1

=> 1 + r = 1.1

A = 80000 ($)

n = 45

FV = A(1 + r)^n = 80000*1.1^45 = 5831239 ($) : Fourth Option (ANSWER)

3.

If interest rate is 10 % and paid monthly :

r monthly = 10/1200 = 1/120

=> 1 + r = 1 + 1/120 = 121/120

A = 80000 ($)

n = 45*12 = 540

FV = A(1 + r)^45 = 80000*(121/120)^540 = 7068334 ($) : Fourth Option (ANSWER)