DSC1630 Assignment 2 Semester 1 2026 - DUE 25 March 2026; 100% CORRECT AND TRUSTED SOLUTIONS

,DSC1630 Assignment 2 Semester 1 2026 - DUE 25 March 2026


Question 1

A loan will be paid back by means of payments of R250 each, every six months
for ten years. An interest rate of 5% per year, compounded every six months,
will be applicable. The present value of the loan is:



Given:
R = 250
j = 5% p.a., compounded semi-annually
i = 0. = 0.025
n = 10 × 2 = 20

Step 1: Identify annuity type

Ordinary annuity (payments at the end of each period)



Step 2: Formula
𝑃𝑉 = 𝑅 × 𝑎ₙ|ᵢ
(1 − (1 + 0.025)−20 )
𝑃𝑉 = 250 × [ 0.025]




Step 3: Calculate
PV = 250 × 15.5892
PV = R3 897,30

Answer: R3 897,30

, Question 2

A nominal interest rate of 19,40% per year, compounded monthly, is equivalent
to a continuously compounded rate.



Given:
jₘ = 19,40% = 0.194
m = 12



Step 1: Formula (conversion to continuous compounding)
𝑐 = 𝑚 × ln (1 + 𝑗ₘ 𝑚)




Step 2: Substitute values
𝑐 = 12 × ln (1 + 0.194 12)
𝑐 = 12 × ln(1.0161667)
𝑐 = 12 × 0.016037



Step 3: Calculate
c = 0.192444

Answer: 19,24% per year (continuous compounding)



Question 3

An amount of money accumulates to R45 946 at a continuous compounding rate
of 8% per year, after 57 months. Find the original amount.