Question

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

Answer 1

Answer:

C. P69,256.82

Step-by-step explanation:

We know that,

The amount formula in compound interest is,

$A=P(1+\frac{r_1}{n_1})^{n_1t_1} (1+\frac{r_2}{n_2})^{n_2t_2}.......$

Where, P is the principal amount,

$r_1, r_2....$ are the annual rate for the different periods,

$t_1, t_2,.....$ are the number of year for different periods,

$n_1, n_2, n_3...$ are the number of periods,

Given,

A = P 200,000,

$r_1=10%=0.1$, $n_1=4$, $t_1=5$,$r_2=12%=0.12$, $n_2=1$, $t_2=5$

Thus, by the above formula the final amount would be,

$200000=P(1+\frac{0.1}{4})^{4\times 5}(1+\frac{0.12}{1})^{1\times 5}$

$200000=P(1+0.025)^{20}(1+0.12)^5$

$200000=P(1.025)^{20}(1.12)^5$

$\implies P=69,256.824\approx 69,256.82$

Option C is correct.