Question

Matt is saving to buy a new motorcycle. If he deposits $70 at the end of each month in an account that pays an annual interest rate of 2.5%, how much will he have in 30 months? Assume that the compounding is being done monthly.

Answer 1

P = $70,  p = 2.5% = 0.025
q = 1 + 0.025 / 12 = 1.002
Future value of a periodic deposit:
A = P · q · ( q^30 - 1 ) / ( q - 1 )
A = 70 · 1.002 · ( 1.002^30 - 1 ) / ( 1.002 - 1 )
A = $2,166
Answer:
He will have $2.166 in 30 months.

Answer 2

Answer

$20,448.6567

Explanation

The rate per month = 2.5%/12

                                  = 0.208333%

The formula  for compound interest is;

Amount = P(1+r)ⁿ   Where p ⇒ deposit+

                                          r ⇒ rate

                                           n ⇒ period

∴ Amount saved after 30 months = 70(1+0.20833)³⁰

                                                         = 70 × 292.1236672

                                                       =  $20,448.6567