Financial Mathematics: Questions and Solutions (Q1-Q20)
Q1:
Ngoako received R2 340 at a 12% discount rate. Find the future value after 10 months.
S = P / (1 - dt) = 2340 / (1 - 0.12 10/12) = .90 = R2 600
Q2:
Invested R1 500 at 6.57% simple interest for 16 months.
A = P(1 + rt) = 1500 (1 + 0.0657 1.333) = R1 631.40
Q3:
Future value R2 599 on 8 Dec, deposited 16 April at 8.5% simple interest.
t = 236/365 0.6466 yrs; P = 2599 / (1 + 0.085 0.6466) = R2 464.21
Q4:
R2 500 now or R2 730 in 4 months. Find simple interest rate.
I = 230, t = 4/12; r = 230 / (2500 0.333) = 27.62%
Q5:
Bank discount rate 12%, future value R5 000 in 6 months.
P = 5000 (1 - 0.12 0.5) = 5000 0.94 = R4 700.00
Q6:
Future value R30 835.42 from R25 000 at 10.5% compounded weekly.
i = 0.105/52, n unknown: n 104.13 weeks 2.00 years
Q7:
Nominal 19.40% compounded monthly continuous compounding equivalent.
r_cont = 12 ln(1 + 0.194/12) 19.25%
Q8:
Fikile deposited R2 500 on 8 Jan 2025, 13.45% compounded monthly, ending 17 Nov.
9 full months: A1 = 2765.25; 16-day simple: A = 2765.25 1.0059 = R2 781.56
Q9:
R4 500 grew to R5 268.24 in 2 years. Effective rate = sqrt(5268.) - 1 = 8.1%
Q10:
Final = R50 000 in 5 yrs at 13.88% compounded weekly.
i = 0.1388/52, n = 260 P = 50000 / (1.002669)^260 = R34 905.25
Q11:
Q1:
Ngoako received R2 340 at a 12% discount rate. Find the future value after 10 months.
S = P / (1 - dt) = 2340 / (1 - 0.12 10/12) = .90 = R2 600
Q2:
Invested R1 500 at 6.57% simple interest for 16 months.
A = P(1 + rt) = 1500 (1 + 0.0657 1.333) = R1 631.40
Q3:
Future value R2 599 on 8 Dec, deposited 16 April at 8.5% simple interest.
t = 236/365 0.6466 yrs; P = 2599 / (1 + 0.085 0.6466) = R2 464.21
Q4:
R2 500 now or R2 730 in 4 months. Find simple interest rate.
I = 230, t = 4/12; r = 230 / (2500 0.333) = 27.62%
Q5:
Bank discount rate 12%, future value R5 000 in 6 months.
P = 5000 (1 - 0.12 0.5) = 5000 0.94 = R4 700.00
Q6:
Future value R30 835.42 from R25 000 at 10.5% compounded weekly.
i = 0.105/52, n unknown: n 104.13 weeks 2.00 years
Q7:
Nominal 19.40% compounded monthly continuous compounding equivalent.
r_cont = 12 ln(1 + 0.194/12) 19.25%
Q8:
Fikile deposited R2 500 on 8 Jan 2025, 13.45% compounded monthly, ending 17 Nov.
9 full months: A1 = 2765.25; 16-day simple: A = 2765.25 1.0059 = R2 781.56
Q9:
R4 500 grew to R5 268.24 in 2 years. Effective rate = sqrt(5268.) - 1 = 8.1%
Q10:
Final = R50 000 in 5 yrs at 13.88% compounded weekly.
i = 0.1388/52, n = 260 P = 50000 / (1.002669)^260 = R34 905.25
Q11:
