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

C. P69,256.82

Explanation:

We know that,

The amount formula in compound interest is,

`A=P(1+(r_1)/(n_1))^(n_1t_1) (1+(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+(0.1)/(4))^(4* 5)(1+(0.12)/(1))^(1* 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.