A father wishes to give his son P200, 000 ten years from now. What amount should he invest if it will earn interest at 10% compounded quarterly during the first five years and 12% compounded annually during the next five years? A. P68,757.82 B. P62,852.23 C. P69,256.82 D. P67,238.54

Accepted Solution

Answer:C. P69,256.82Step-by-step explanation:We know that,The amount formula in compound interest is,[tex]A=P(1+\frac{r_1}{n_1})^{n_1t_1} (1+\frac{r_2}{n_2})^{n_2t_2}.......[/tex]Where, P is the principal amount,[tex]r_1, r_2....[/tex] are the annual rate for the different periods,[tex]t_1, t_2,.....[/tex] are the number of year for different periods,[tex]n_1, n_2, n_3...[/tex] are the number of periods,Given,A = P 200,000,[tex]r_1=10%=0.1[/tex], [tex]n_1=4[/tex], [tex]t_1=5[/tex],[tex]r_2=12%=0.12[/tex], [tex]n_2=1[/tex], [tex]t_2=5[/tex]Thus, by the above formula the final amount would be,[tex]200000=P(1+\frac{0.1}{4})^{4\times 5}(1+\frac{0.12}{1})^{1\times 5}[/tex][tex]200000=P(1+0.025)^{20}(1+0.12)^5[/tex][tex]200000=P(1.025)^{20}(1.12)^5[/tex][tex]\implies P=69,256.824\approx 69,256.82[/tex]Option C is correct.