Question

1) A personal account earmarked as a retirement supplement contains $242,100. Suppose $200,000 is used to establish an annuity that earns 5%, compounded quarterly, and pays $4500 at the end of each quarter. How long will it be until the account balance is $0? (Round your answer UP to the nearest quarter.)

2) A recent graduate's student loans total $13,000. If these loans are at 4.4%, compounded quarterly, for 8 years, what are the quarterly payments? (Round your answer to the nearest cent.)

3) For equipment upgrades, a business borrowed $300,000 at 8% compounded semiannually for 5 years. What are the semiannual payments (in dollars)? (Round your answer to the nearest cent

Answer 1

1) A personal account earmarked as a retirement supplement contains $242,100. Suppose $200,000 is used to establish an annuity that earns 5%, compounded quarterly, and pays $4500 at the end of each quarter. How long will it be until the account balance is $0? (Round your answer UP to the nearest quarter.)

We can use PV of an Annuity formula to calculate the period of periodic payment from deposit

PV = PMT * [1-(1+i) ^-n)]/i

Where,

Present value (PV) =$200,000

PMT = Quarterly payment =$4500

n = N = number of payments =?

i = I/Y = interest rate per year = 5%, quarterly interest rate = 5%/4 = 1.25%

Therefore,

$200,000 = $4500* [1- (1+0.0125)^-n]/0.0125

Or n = 65.28 or 65 payments

2) A recent graduate's student loans total $13,000. If these loans are at 4.4%, compounded quarterly, for 8 years, what are the quarterly payments? (Round your answer to the nearest cent.)

We can use PV of an Annuity formula to calculate periodic payment from deposit

PV = PMT * [1-(1+i) ^-n)]/i

Where,

Present value (PV) =$13,000

PMT = Quarterly payment =?

n = N = number of payments = 8 *4 = 32

i = I/Y = interest rate per year = 4.4%, quarterly interest rate = 4.4%/4 = 1.1%

Therefore,

$13,000 = PMT* [1- (1+0.011)^-32]/0.011

PMT = $484.14

3) For equipment upgrades, a business borrowed $300,000 at 8% compounded semiannually for 5 years. What are the semiannual payments (in dollars)? (Round your answer to the nearest cent

The semiannual payments can be calculated with the help of following formula

We can use PV of an Annuity formula to calculate the periodic payment of loan amount

PV = PMT * [1-(1+i) ^-n)]/i

Where,

Loan amount (PV) =$300,000

PMT = Semiannual payment =?

n = N = number of payments = 5 *2 = 10

i = I/Y = interest rate per year = 8%, semiannual interest rate = 8%/2 = 4%

Therefore,

$300,000 = PMT* [1- (1+0.04)^-10]/0.04

PMT = $36,987.28