Question

Uncle Larry would like to supplement his pension so he calls his insurance company to find out about his options.
He is told that he could pay $750 every quarter for ten years (making 10×4 = 40 payments at the end of each quarter
until his retirement; first payment due one quarter from today) and then he will start receiving quarterly payments of
$1,000 forever. He will receive the first $1,000 in ten years and one quarter, i.e. one quarter after he made his last
payment; after he passes away his heirs (and their heirs, etc.) will continue to receive the quarterly payments forever.
What is the effective annual rate (EAR) the bank used to calculate the terms of this deal?

Answer 1

B 3 Let us assume periodic rate x 5 750 * [ (1 + x)^40 - 1)/x] (1 + x)^40 - 1) 6. = 1000/x = 1000/750 (1 + x)^40 2.33 %3D (1 + x) 1.0214084 %3D 10 2.14% %3D 11 EAR 12 8.84% 13

1 2 3 Let us assume perio 4 750 * [ (1 + x)^40 - 1 (1 + x)^40 - 1) =1000/750+1 (1 + x)^40 =D8^(1/40) (1 + x) %3D 10 =D9-1 х 11 =(1+D10)^4-1 12 EAR 13 14 15 16 17 18 19 20