Question

11. [-/0.1 Points] DETAILS TANAPMATHS 4.2.022 MY NOTES PRACTICE ANOTHER Luis has $140,000 in his retirement account at his present company. Because he is assuming a position with another company, Luis is planning to roll over his assets to a new account. Luis also plans to put $3500/quarter into the new account until his retirement 30 yr from now. If the account earns interest at the rate of 7%./year compounded quarterly, how much will Luis have in his account at the time of his retirement? Hint: Use the compound interest formula and the annuity formula. (Round your answer to the nearest cent.) $ Need Help? Read Talk to Tutor MY NOTES PRACTICE ANOTHER 12. [-/0.1 Points) DETAILS TANAPMATHS 4.2.024.MI. Lupe made a down payment of $1600 toward the purchase of a new car. To pay the balance of the purchase price, she has secured a loan from her bank at the rate of 12%/year compounded monthly. Under the terms of her finance agreement she is required to make payments of $230/month for 60 mo. What is the cash price of the car? (Round your answer to the nearest cent.) $ Need Help? Read Master 1 Talk te Tutor

Answer 1

11]

Future value of lump sum = present value * (1 + (r/n))^n*t

where r = annual rate of interest,

n = number of compounding periods per year

t = number of years

Future value of today's assets = $140,000 * (1 + (7%/4))^4*30

Future value of today's assets = $1,122,685.68

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. This is $3,500

r = periodic rate of interest. This is (7%/4). We divide by 4 since we need to convert the annual rate into quarterly rate)

n = number of periods. This is 30 * 4 = 120 (there are 120 quarters in the investment period)

Future value of annuity = $3,500 * [(1 + (7%/4))¹²⁰ - 1] / (7%/4)

Future value of annuity = $1,403,836.69

Value of account at retirement = future value of today's assets + future value of annuity

Value of account at retirement = $1,122,685.68 + $1,403,836.69

Value of account at retirement = $2,526,522.37

12]

cash price = down payment + loan amount

Loan amount is calculated as :

PV of annuity = P * [1 - (1 + r)^-n] / r,

where P = periodic payment. This is $230

r = interest rate per period. This is (12%/12) = 1%. We divide by 12 to convert the annual rate into monthly rate.

n = number of periods. This is 60.

PV of annuity = $230 * [1 - (1 + 1%)^-60] / 1%

PV of annuity = $10,339.66

Loan amount = $10,339.66

cash price = down payment + loan amount

cash price = $1,600 + $10,339.66

cash price = $11,939.66