Question

Suppose that you have an initial investment of $350. For each of the given compounding situations, using an annual percentage rate (APR) of 1.5% find the value of the investment after 22 months, find how long it would take to double the money, and find the APY. Follow the rounding rules at the top of the column and include units in your answers. Compounded Formula entered in Y1 Value after 22 months (to the nearest cent) Time it takes to double initial investment APY (rounded to 3 decimal places) Semiannually (Hint: When was the last time interest was credited to the account) 350(1+015 j2(t) |$359.3 4_yrs 4 mos 1.506 Quarterly 350(1+015)"(t) $350.0 mos Monthly Continuously YTS mos (in years, correct to 3 decimal places) Vrs

the answers i already have are probably wrong. please correct if so. thank you!!!

Answer 1

Formula to be entered in year 1:

A = P(1+

Where,

P = Initial Investment Principal
r = APR
n = number of times interest is compounded (i.e semiannually is 2, quarterly is 4, etc)
t = time in years

Part 1:

In the given scenario,
P = 350
r = 0.015
n = Semiannually i.e 2
t = 22 months i.e 1.8334 years

Therefore formula is:

0.015. A = 350(1+ 21.8334

Therefore, value after 22 months is = $359.72

Time taken to double initial investment is

Therefore, we know that A = 2*350 (i.e double)

Therefore, using the same main equation as above, we can arrive at

as T is the time which we have to find

0.015 (350) * 2) = 350 (1+ - می 2

0.015, 2 = (1+ بری

2=(1+0.0075) +t

2 = (1.0075)2t

at this stage, we need to apply log. Therefore we will arrive at

log 2 = log(1.0075)2*t

log 2 = 2t log(1.0075)

Log 2 = 0.301 and log 1.0075 = 0.0032

0.301 = 2t * 0.0032

0.301 2t = 00032

2t = 94.0625

t = 47.03125

That is 47 years and 0.38 months (11 days)

APY is computed by the following formula

APY = (1+-)" - 1

where,
r= annual interest rate i.e 1.5% or 0.015
n = number of times interest is compounded (i.e semiannually is 2)

Therefore, we can compute APY as follows:

APY = (1, 0.015

APY = (1 +0.0075)2 - 1

APY = (1.0075)2 - 1

APY = 1.01506 - 1

or 1.506%

APY = 0.01506

Part 2:

In the given scenario,
P = 350
r = 0.015
n = Quarterly i.e 4
t = 22 months i.e 1.8334 years

Therefore formula is:

0.015 A = 350(1+2 24*1.8334

Therefore, value after 22 months is = $359.74

Time taken to double initial investment is

as T is the time which we have to find

10.015 (350 +2)= 350(1+2

2 = (1 + 0.015 $0)4

2 = (1 + 0.00375) **t

2 = (1.00375)4+t

at this stage, we need to apply log. Therefore we will arrive at

log 2 = log(1.00375) **t

log 2 = 4t log(1.00375)

Log 2 = 0.301 and log 1.00375 = 0.00163

0.301 = 4 * 0.00163

0.301 4t 00163

4t = 184.6626

t = 46.1656

That is 46 years and 2 months

APY is computed by the following formula

APY = (1+-)" - 1

where,
r= annual interest rate i.e 1.5% or 0.015
n = number of times interest is compounded (i.e Quarterly is 4)

Therefore, we can compute APY as follows:

APY = (1+

APY = (1 +0.00375) - 1

APY = (1.00375)4 - 1

APY = 1.01508 - 1

or 1.508%

APY = 0.01508

Part 3:

In the given scenario,
P = 350
r = 0.015
n = Monthly i.e 12
t = 22 months i.e 1.8334 years

Therefore formula is:

4 = 350(1+- 0.015 2,12+1.8334 <1 15

Therefore, value after 22 months is = $359.75

Time taken to double initial investment is

as T is the time which we have to find

| 0.015 (350 +2)= 350(1+2

0.015 2 = (1+1

2 = (1+0.00125) 12+t

2 = (1.00125) 12t

at this stage, we need to apply log. Therefore we will arrive at

log 2 = log(1.00125) 12*t

log 2 = 12t log(1.00125)

Log 2 = 0.301 and log 1.00125 = 0.00054

0.301 = 12t * 0.00054

12t = 0.301 0.00054

12t = 557.4074

t = 46.45062

That is 46 years and 6 months

APY is computed by the following formula

APY = (1+-)" - 1

where,
r= annual interest rate i.e 1.5% or 0.015
n = number of times interest is compounded (i.e Monthly is 12)

Therefore, we can compute APY as follows:

0.015、 APY = (1+ - 1972

APY = (1 + 0.00125)12 - 1

APY = (1.00125)12 - 1

APY = 1.01508 - 1

or 1.510%

APY = 0.01510

Part 4:

In case of compounded continuously, the formula to be entered is year 1 is

A = Pert

Where,
P = Initial Investment Principal i.e 350
e = Mathematical constatnt
r = APR i.e 1.5% or 0.015
t = time in years i.e 1.8334 years

Therefore,

the value of e^0.0275 = 1.02788

Therefore,

A= 350 * 1.02788

A=359.76

The simplified formula to compute time taken to double investment in case of continuous compounding is

In (2) t=

the value of ln(2) = 0.693
r = 0.015

therefore,

$t = \frac{0.693}{0.015}$

years

APY is computed by the following formula

the value of e^0.015 = 1.01511

or 1.511%