Ming borrows X for 10 years at an annual effective interest rate of 8%. If he pays

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