Answer to Question #316279 in Finance for Helen

Question

6.) A social worker deposits a uniform amount of P12,000 at the end of each year in order to get a lump sum of money by the time she will retire at the end of 20 years. If the compound amount factor for this annuity is equal to 36.78559.

1. Compute the nominal interest rate.

2. Determine how much will she receive at the end of 20 years.

3. Determine the worth of the sinking fund factor in this fund invested.

Ans. 1. 6% 2. P441,427.08 3. 0.027184557

Answer 1

$A=P(1+\frac{r}{100})^{12}$

compound amount factor= $36.78559$

$(1+\frac{r}{100})^{12}=36.78559\\r=6\%$

Amount after 20 years

$A=P(1+\frac{r}{100})^{nt}\\A=12,000(1+\frac{0.06}{12})^{120} \\A=441,427.08$

sinking fund factor

A= [(1+(r/m))^n*m-1] / (r/m) * P

=((1+6%/12) ^(12-12) – 1)/(6%/12) * 12,000

=0.027184557