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Homework answers / question archive / 1) Rebecca borrows $30,000 at 5% interest
1) Rebecca borrows $30,000 at 5% interest. a) Find her annual payment if she uses amortization over 10 years and makes level payments at the end of each year. b) How much interest would Rebecca pay using this method? c) Find her annual cost if she pays the bank the interest due on the outstanding balance at the end of every year and makes annual contributions to a sinking fund earning 7% interest with the intention of paying off the loan at the end of 10 years. d) Rebecca decides to set her total annual cost to the loan payment amount calculated in part a). She pays the interest each year and invests the balance in her sinking fund. How much does she have left in the sinking fund once she pays off the loan? [10 points)
2) On January 1, 2018, Yves invests $50,000 to a mutual fund investing in a mix on stocks and bonds. Balances and cashflow amounts from 2018-2020 are shown below. Note that he makes no further deposits in 2018 or 2019 but makes two deposits in 2020. Date Cashflow January 1, 2018 December 31, 2018 December 31, 2019 May 1, 2020 August 31, 2020 December 31, 2020 +$50,000 $0 $0 +$5,000 +$8,000 $0 Account Balance After Cashflow $50,000 $52,368 $55,059 $58,843 $68,157 $69,863 a) Find his annual effective return in 2019 b) Find his average effective annual return over 2018-9. c) Find the amount of investment income earned in 2020. d) Find his time weighted rate of return for 2020. e) Find his dollar weighted rate of return for 2020. (10 points)
Answer 1
loan amount (PV)=30000
monthly rate (i) =5%
number of years (n) =10
equal or annuity Payment formula = PV* i *((1+i)^n)/((1+i)^n-1)
30000*5%*((1+5%)^10)/(((1+5%)^10)-1)
=3885.137249
So level payment each year will be $3885.14
b
Total interest cost = (level payment each year *numbe of payment)-loan amount
=(3885.14*10)-30000
=8851.4
So interest paid during this method is $8851.4 during the life of loan
c
interest paid each year = loan * interest rate
=30000*5%
=1500
Sinking fund amount to be paid will be calculated using annuity for future value accumulation formula
Amount of repayment or future value = 30000
interest rate (i) =7%
number of years (n) =10
Sinking fund deposit formula = Future value*i/(((1+i)^n)-1)
=30000*7%/(((1+7%)^10)-1)
=2171.325082
total annual cost = interest cost + sinking fund deposit
=1500+2171.325082
=3671.325082
Total annual cost in this method is $3671.33
d
Annual cost is maintained as equal payment in part a =3885.14
interest cost paid each year = 30000*5% = 1500
Balance to de deposited in sinking fund (P)= 3885.14-1500
=2385.14
number of deposit (n) =10
interest rate (i)=7%
Amount accumulated at end of 10th period will be calculated using future value of annuity formula
future value of annuity formula = P*(((1+i)^n)-1)/i
2385.14*(((1+7%)^10)-1)/7%
=32954.16269
loan amount repayment = 30000
Balance saved = 32954.16269-30000
=2954.16269
So balance left in sinking fund is $2954.16 after 10 years
