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Can you explain to me why we're able to add the accumulated amount of 1000 invested for 5 years to the additional accumulated value of 1000 they invested after 3 years?

JMP
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John van Zalk
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  • Both payments of Investor A have the same reference date, $t=5$ This is the condition that the payments can be added.

    Payment 1 is is made at $t=0$ and it is compounded five years. This is the future value of payment 2 at $t=5$.

    Payment 2 is is made at $t=3$ and it is compounded two years ($=2\cdot 8$ quarters). This is the future value of payment 2 at $t=5$.

    The sum is the future value of both payments at $t=5$

     – callculus42 Feb 02 '23 at 18:31

1 Answers1

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After $3$ years, there is

$$1000\cdot 1.01^{12}$$

in the account. Another $1000$ is deposited, and interest is applied for a further $2$ years:

$$\left(1000\cdot 1.01^{12}+1000\right)\cdot 1.01^{8}$$

This can be written as

$$1000\cdot 1.01^{12}\cdot 1.01^{8}+1000\cdot 1.01^{8}$$

$$=1000\cdot 1.01^{20}+1000\cdot 1.01^{8}$$

as in the solution.

JMP
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