Answer to Question #197945 in Financial Math for Beauty Magadlela

Question

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

Answer 1

[5] none of the above

This is a future annuity due which will be given by

Future Value of an Annuity

Due (FVAD) Formula$=A×\frac{(1 + r)^n - 1}{r}+A(1 + r)^n-A$

A = the annuity payment , r = the interest rate per time period, and n = the number of time periods.

Substituting values

$S=X×\frac{(1 + \frac{k}{12})^{24} - 1}{\frac{k}{12}}+X(1 + \frac{k}{12})^{24}-X$ in this case S =future value X = the annuity payment or periodic rent, k= the interest rate per time period, and 24 = the number of time periods.