Loans, investments & annuities

Jemaia invested $12 500 into an account that pays compound interest at the rate of 7.8% per annum, compounding monthly.

a) Construct a recurrence relation model for the balance of Jemaia’s investment after n months.

b) Apply the recurrence relation to determine the balance of Jemaia’s investment after 4 months.

Eva borrows $15 000 and will be charged compound interest at the rate of 4.6% per annum.

a) Calculate the balance of the loan after 2 years.

b) What is the total interest that will be charged after two years?

Ash has started working and can save $400 per month to put towards buying a dinghy. If his investment returns an annuity of 4.89% p.a. paid monthly, how much money will he have in 3 years?

Using the effective interest rate formula calculate the effective interest rate for 7.5% p.a. compounding monthly.

Ella is saving for a new car and wants to invest the money she has saved. She is offered the following rates from different banks:

Offer 1: 5.4% p.a. compounded weekly

Offer 2: 5.3% p.a. compounded daily

Offer 3: 5.6% p.a. compounded monthly

Which offer will give Ella the best return?

Anastacia deposits $4000 into an account that pays interest at 4.9% p.a. compounded monthly. She also makes a deposit of $250 at the end of each month. How much will Anastacia have in this account at the end of 5 years?