Someone wants you to lend her 3000 today She promises to pay

Someone wants you to lend her $3000 today. She promises to pay you $1000 one year from today, $1050 two years from today and $1100 three years from today. Alternatively, you can earn 3% compounded annually by putting the money in a savings account. Should you lend her the money?  How large should the last payment be, the first two being the same as in part 1, for you to be willing to lend her the money?

Solution

For a better understanding, lets consider how much money will you be having after 3 years in both the circumstances ( lending her money and not lending her)

1) you don\'t lend her $3000 and deposit it in bank at 3% annual interest.
at the end of 3 years you\'ll have :-
= $3000 (1+ 3%)³

= $3000 (1.03)³

⁼ $3000 (1.0927) = $3278.1

2) you lend her money :-

at the end of one year you\'ll have

= $1000

at the end of 2nd year, you\'ll have

= $1000(1.03)² + $1050 =$2080

at end of 3rd year you\'ll have

= $2080 (1.03)¹ + $1100 = $3142.4

By above analysis we can see that, lending money to her wouldn\'t be a good option instead you should deposit it in bank. You\'ll receive $135.7 ($3278.1 -$3142.4) more, if you deposit money in bank than if you lend her.

If she agrees to pay $1235.7 ($1100 + $135.7), then you should lend her money.

Note:- it is assumed that, you don\'t hold ideal cash with you, you deposit it in bank on compoundly basis, whenever you receive amount from her.

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