Question

​(Compound interest with​ non-annual periods)  Calculate the amount of money that will be in each of the following accounts at the end of the given deposit​ period:

Account Holder	Amount Deposited			Annual Interest Rate		Compounding Periods Per Year​ (M)		Compounding Periods​ (Years)
Theodore Logan III	​$	1,100		12	​%	12		10
Vernell Coles		94,000		10		2		3
Tina Elliot		8,000		12		4		5
Wayne Robinson		118,000		12		1		4
Eunice Chung		32,000		12		6		4
Kelly Cravens		13,000		12		3		5

Answer 1

The general formula to calculate accumulated value at the end of the period is:

here AV is the accumulated value, PV is the initial amount deposited, r is the rate of interest, n is the number of years, m is the compounding periods per year

So,

For Theodore Logan III,

AV = $1,100(1+0.12/12)^12*10

= $1,100(1+0.01)¹²⁰

= $1,100(1.01)¹²⁰

Using Calculator we find the value of (1.01)¹²⁰

= $1,100*3.300

= $3,630

For Vernell,

AV = $94,000(1+0.10/2)^2*3

= $94,000(1+0.05)⁶

= $94000(1.05)⁶

Using Calculator we find the value of (1.05)⁶

= $94000*1.34009

= $125968.99

For Tina,

AV = $8000(1+0.12/4)^4*5

= $8000(1+0.03)²⁰

= $8000(1.03)²⁰

Using Calculator we find the value of (1.03)²⁰

= $8000*1.80611123

= $14448.89

For Wayne,

AV = $118000(1+0.12/1)^1*4

= $118000(1+0.12)⁴

= $118000(1.12)⁴

Using Calculator we find the value of (1.12)⁴

= $118000*1.57351936

= $185675.28

For Eunice,

AV = $32000(1+0.12/6)^6*4

= $32000(1+0.02)²⁴

= $32000(1.02)²⁴

Using Calculator we find the value of (1.02)²⁴

= $32000*1.60843

= $51469.99

For Kelly

AV = $13000(1+0.12/3)^3*5

= $13000(1+0.04)¹⁵

= $13000(1.04)¹⁵

Using Calculator we find the value of (1.04)¹⁵

= $13000*1.800943

= $23412.26