Question

A person puts $400.00 into a savings account with 2.4% annual interest rate (computed continuously). The value of such an investment is given by: V=Pe(rt), where P is principal invested, r is the annual interest rate, and t is the number of years receiving interest. How many years are required before the total interest is increased by > $1.00 due to compounding interest? Round up to the nearest whole year. Without compounding, the total interest amount would have been P r t.

V Pe(rt)

For convenience, the credit union provided the following table of the exponential function:

r t	V
0.024	1.0243
0.048	1.0492
0.072	1.0747
0.096	1.1008
0.120	1.1275
0.144	1.1549

A) 1

B) 2

C) 3

D) 4

E) 5

F) 6

Answer 1

Here we apply formula for compound interest as well as simple interest.

function ot Gven alue o tment xate Cu dntereut ie Perd Y= 3afe afhferest PEPincipal oyear

Wthaut apoundastexert 400)Caa24) t Gten O-024F +) 400 Le 9.63 O024t /400 e for t1eax O-O24 e -+0.002s 024 RHS LHs t2years 0.048 O48 - +(D.0025 11 Cado year dcoreat
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