Question

Bob borrows 540,000 at annual effective interest rate 3%. She repays this loan by paying off only the interest due at the end of each year to the lender and depositing a level amount Q at the end of each year into a sinking fund account paying 6% APY. The goal is to accumulate the full balance of the loan amount in the sinking fund at the end of 10 years.

a. Find the level sinking fund deposit.

b. What rate (AEIR) does Anita end up paying on this loan?

c. What is the lender’s APY?

Answer 1

Fv

Amount of Principal at end of 10years

540,000

Rate

Interest rate in sinking fund account

6%

Nper

Number of years of deposit

10

PMT

Level deposit at end of each year

40,969

(Using PMT function of excel with Rate=6%, Nper=10, Fv=-40000)

Q=40,969

a

Sinking Fund Deposit

40,969

b

AnnualEffective Interest Rate;

Annual interest payment=540000*3%

16,200

Annual Sinkingb Fund Deposit

40,969

Pmt

Total Annual Cash Outflow

57,169

Pv

Initial Cash inflow

540,000

Nper

Number of years of annual cash outflow

10

RATE

Annual Effective Interest Rate;

1.05%

(Using RATE function of excel with Nper=10,Pmt=57169,Pv=-540000, )

c

Lender's APY

3%

Pv

Amount of Initial cash outflow

540,000

Pmt

Annual   payment received

16,200

Nper

Number of years

10

Fv

Terminal payment received at end of 10 years

540,000

RATE

Lenders APY

3%

(Using RATE function of excel with Nper=10,Pmt=16200,Pv=-540000,Fv=540000 )