Question

£250 is invested in a saving account. The nominal rate convertible monthly for the first 3 months is 18% and the nominal rate of interest convertible quarterly for the next 9 months is 20%. How much is in the account at the end of the year?

Answer 1

solution

For the first 3 months:

$$Annual\ rate =18\%$$

The rate convertible monthly is:

$$\frac{18 \%}{12} = 0.015$$

The number of compounding periods in the 3 months is 3

For the next 9 months:

$$Annual\ rate =20\%$$

The rate convertible quarterly is:

$$\frac{20 \%}{4} = 0.05$$

The number of compounding periods in the 9 months is:

$$\frac{9}{12}*4=3$$

Therefore the investment grows by 0.015 for 3 periods and then by 0.05 for a further 3 periods.

$$Future \ value = P*(1+r_1)^{n1}*(1+r_2)^{n2}$$

$$= 250*(1.015)^{3}*(1.05)^{3}=302.6259$$

answer: the investment will be worth £ 302.63