Financial Math Answers

Find the present value of the following annuities. Assume the discounting occurs once a year A. The customer agreed to pay rent at the end of each year and the landlord charges $21,600 per year . The required rate of return of the landlord is 6.85%. The rent contract will last for 7 years Required: Find the present value of this agreement for the landlord B. A customer approached a car sales agent and makes a car lease agreement for 6 years. The cash flow [annual] is $6000. The agent charges 7.2% interest on such contract Required: How much will be the present value of such an agreement ?

Mr Mahlangu invests R20000 to play lobola. After 48 months he receives 65000. The interest on the investment is compounded quarterly. Determine the yearly interest rate at which money was invested. Give your answer as a percentage rounded to two decimal places.

i) If Rs.64 amount to Rs.83.20 in 2 years, what will Rs.86 amount to in 4 years at the same rate 

of simple interest?

Frieda will discharge a debt of R500 000 six years from now, using the sinking fund method. The interest of the debt is 15,6% per year, paid quarterly. The sinking fund earns interest at a rate of 8,4% per year, compounded monthly.

The total yearly cost to discharge the debt (to the nearest rand) is

[1] R142 375.

[2] R42 000.

[3] R78 000.

[4] R93 834.

[5] R128 833.

Frieda will discharge a debt of R500 000 six years from now, using the sinking fund method. The interest of the debt is 15,6% per year, paid quarterly. The sinking fund earns interest at a rate of 8,4% per year, compounded monthly.

The monthly deposit into the sinking fund is

[1] R12 958,53.

[2] R10 736,10.

[3] R5,364,60.

[4] R4 236,10.

[5] R16 235,96

You are saving to pay for your children’s university costs in 20 years’ time. In the first year, your payment is R3 600, after which your yearly payments increased by R360 each year. If the expected interest rate per year is 10%, the amount that you expect to receive to the nearest rand on the maturity date will be

[1] R213 030.

[2] R340 380.

[3] R412 380.

[4] R484 380.

[5] none of the above. 

Bonita intends to open a small fabric shop and borrows the money for it from her aunt Magda. Bonita feels that she will only be able to start repaying her debt after three years. Bonita will then pay aunt Magda R105 000 per year for five years. Money is worth 19,5% per year.

The amount of money that aunt Magda originally lent Bonita is

[1] R130 288,26.

[2] R186 054,89.

[3] R184 589,43.

[4] R98 346,23.

[5] R130 633,09

Bonita intends to open a small fabric shop and borrows the money for it from her aunt Magda. Bonita feels that she will only be able to start repaying her debt after three years. Bonita will then pay aunt Magda R105 000 per year for five years. Money is worth 19,5% per year.

The present value of Bonita’s debt at the time she will start paying aunt Magda back is

[1] R408 978,93.

[2] R317 500,78.

[3] R222 924,04.

[4] R525 000,00.

[5] R436 649,07.

Percy deposits R100 into a bank account earning interest at an interest rate of 18% per annum, compounded monthly. The time (in months) that it will take the account to accumulate to R20 000 is given by

[1] n = ln[200(1,015)] 0,015 .

[2] n = ln[200(0,015) + 1] ln(1 + 0,015) .

[3] n = ln[200(1,015) + 1] − ln(1,015).

[4] n = ln[200(0,015) − 1] ln(1 + 1,015) .

[5] none of the above.

At the beginning of each month an amount of X rand is deposited into a savings account earning k × 100% interest per year, compounded monthly. The future value of these savings after 24 deposits can be denoted by

[1] S = X(1 + k 12 ) 24 .

[2] S = (1 + k 12 )Xs 24 k÷12.

[3] S = Xs 24 k .

[4] S = (1 + k)Xs 24 k .

[5] none of the above