Ming borrows X for 10 years at an annual effective interest rate of 8%. If he pays the principal and accumulated interest in one lump sum at the end of 10 years, he would pay 468.05 more in interest than if he repaid the loan with 10 level payments at the end of each year. Calculate X.

X = $700

Explanation:

the future value of X = X · (1 + 8%)¹⁰ = 2.158925X

X = annual payment · 6.7101 (PV annuity factor, 8%, 10 periods)

annual payment = X / 6.7101

2.158925X = 10 annual payments + 468.05

2.158925X = 10X/6.7101 + 468.05

2.158925X = 1.490291X + 468.05

0.668634X = 468.05

X = 468.05 / 0.668634 = $700

if you payback the loan in one lump sum at the end of 10 years, you will pay = $700 x 2.158925 = $1,511.25

or you could make 10 annual payments = $700 / 6.7101 = $104.32, in total you would pay $1,043.20

the difference between both = $1,511.25 - $1,043.20 = $468.05

answer assertive;

two years ago, when picking flowers in the mountains back of yosemite valley, i found a book. it was blotted and storm-beaten; all of its outer pages were mealy and crumbly. the paper seemed to dissolve like the snow beneath which it had been buried, however; many of the inner pages were well preserved. and although all were more or less stained and torn, whole chapters were easily readable. this is the condition of the great open book of yosemite glaciers today; its granite pages have been torn and blurred by the same storms that wasted the castaway book.

two years ago, when picking flowers in the mountains back of yosemite valley; i found a book. it was blotted and storm-beaten, all of its outer pages were mealy and crumbly. the paper seemed to dissolve like the snow beneath which it had been buried, however, many of the inner pages were well preserved. and although all were more or less stained and torn; whole chapters were easily readable. this is the condition of the great open book of yosemite glaciers today, its granite pages have been torn and blurred by the same storms that wasted the castaway book.