Investment 2

Jack invested $5000 in a 5-month term deposit at 4.7% pa. At the end of the five months, Jack reinvested the maturity value from the first deposit into an 11-month term deposit at 7.3% pa. What is the maturity value at the end of the second term deposit?

Correct answer:

c =  5436.64 USD

Step-by-step explanation:

$$\begin{gathered} a=5000\text{USD} \\ {p}_1=100\%+4.7\%=1+\frac{4.7}{100}=1.047 \\ {p}_2=100\%+7.3\%=1+\frac{7.3}{100}=1.073 \\ {q}_1=p_1^{1/12}=\sqrt[12]{1.047}\doteq 1.0038 \\ {q}_2=p_2^{1/12}=\sqrt[12]{1.073}\doteq 1.0059 \\ b=a\cdot q_1^5=5000\cdot 1.0038^5\doteq 5096.6067\text{USD} \\ c=b\cdot q_2^{11}=5096.6067\cdot 1.0059^{11}=5436.64\text{USD} \end{gathered}$$

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