Hi Experts, please help me with these questions, I'm very confused of what equation to use. please provide a full explanation.

Lotus and Peter McDonald are preparing to purchase their first house and have managed to save some money. However, although they have these funds, they still need to come up with more money to make up 20% of the deposit, which amounts to $40,000.

After much discussion with their family, they have come up with these two possible options:

Option 1 - Borrow money from Lotuss aunt, Pat.

Option 2 - Peters Dad, Jackson, will take out a loan on their behalf.

Ignore any transaction costs and tax involved in buying a house.

Required:

(a) Option 1 Pat (Lotuss aunt): Using the relevant interest factor table, calculate the following (round your answers to two decimal places):

(i) Lotuss aunt, Pat, has offered to lend them the $40,000 and she is happy for the loan and interest to be repaid 10 years later. If Lotus and Peter borrow the money from Pat, they will have to repay the amount of $58,870 (which includes the principal amount of the loan and the interest). What rate of interest, compounded annually, would Lotus and Peter be paying on the 10-year loan? How much interest would they have paid on the loan?

(ii) If Pat asks Lotus and Peter to repay the loan as an annual equal amount at the end of each year over the 10-year period based on the annual rate of interest calculated from a(i), how much would the annual repayment be? What is the total cash repayment for the loan over the period? How much interest would they have paid on the loan?

(b) Option 2 Jackson (Peters Dad). Using the relevant interest factor table, calculate the following (round your answers to two decimal places):

(i) Jackson is willing to borrow the $40,000 from his bank (Western Bank) on their behalf with an interest rate of 8% p.a. compounding quarterly. The loan and the interest are to be repaid 5 years later. If Jackson borrows the money from the bank, how much will he pay the bank in 5 years time?

(ii) Jackson decided to find out from another bank (SSC Bank) under what conditions they were willing to lend the money to him. If he borrowed $40,000, they would charge an interest rate of 4% p.a. compounded semi-annually. The loan and interest will have to be repaid to the bank over the 5 years with equal payments needing to be made at the beginning of each period. If Jackson borrows the money from this bank, what will be the semi-annual payments that he will make? What is the total cash repayment for the loan over the period? How much interest would he have paid on the loan?

(c) Based on your answers to the above questions for options 1 and 2, make a recommendation to Lotus and Peter as to which option they should choose and explain why?

Here is a Interest factortable

Table 1 - Future Value Interest Factor for one dollar compounded at r percent for n periods: FVIFr,n = (1+r )n

Table 2 - Present Value Interest Factor for one dollar discounted at r percent for n periods: PVIFr,n = 1/(1+r )n

Table 3 - Future Value Interest Factor for a one dollar annuity compounded at r percent for n periods: FVIFAr,n = [(1+r )n - 1]/r

Table 4 - Present Value Interest Factor for a one dollar annuity discounted at r percent for n periods: PVIFAr,n = [1-1/(1+r )n ]/r