Question

5. Wai Ling invests $3,587 at 2% pa simple interest and this investment grows over time to $3,677.81. Calculate the time period (t) over which Wai Ling made the investment. Give your answer in days rounded to the nearest day.

t =                days

6. Calculate the discounted (present) value (P) at 9.69% pa simple interest of a payment of $67,000 due at the end of 3 months. Give your answer in dollars and cents to the nearest cent.

P = $

7. If $80,000 is paid at the end of each year for 15 years, calculate the equivalent single payment now (P) if interest is 20% pa effective. Give your answer in dollars and cents to the nearest cent.

P = $

8. An amount of $4,000 is invested on 27 August 2019 at 6% pa compounded quarterly. Calculate the interest (I) earned between 27 August 2022 and 27 August 2025. Give your answer in dollars and cents to the nearest cent.

I = $

9. Calculate the amount of money that a person must have in a bank today (the beginning of the year) to be able to withdraw $850 at the end of each month for the next 10 years if the bank pays interest compounded monthly at j12 = 14.5% pa. Give your answer in dollars and cents to the nearest cent.

Account balance = $

10. Calculate the amount of money you should invest now, in an account earning 6.1% pa simple interest, in order to have $10,000 after 1 months. Give your answer in dollars and cents to the nearest cent.

Amounted invested = $

Answer 1

P = 3587, A = 3677.81

> I = 90.81

> 90.81 = 3587*.02*t

> t = 1.26 years

Or, 462 days.

Formula for CI, A = P*(1+r/n)^nt

> P = 67000/(1+9.69%/4)^1/4

>   = 65,415.31

Present Value of Annuity = P*(1-(1+r)^-n)

                                                                r             

>                                                  80,000*((1-(1+0.2)^-15/0.2)       

>                                             = 374,037.81

Formula for CI, A = P*(1+r/n)^nt

On 27^th 2022, A = 4,000*(1+6%/4) ^4*3 = 4782.47

On 27^th 2022, A = 4,000*(1+6%/4) ^4*6 = 5718.01

> Interest between the two period = 935.54

Compound interest of 14.5% in terms of SI is equal to (1+.145/12) ¹² – 1 or 15.5%.

Formula for P = EMI/( I x ((1 + r) ⁿ)/ (t x ((1 + r) ⁿ)- 1))

>                       = 850/((15.5%*(1+1.292%)¹²⁰ )/((12*(1+1.292%)¹²⁰ )-1))

                          = 64,616.57                              

A = 10,000 = P*(1+r*t) = P(1+(6.1%*1/12))

> P = 9949.42