Question

For a deposit of ​$1027 at 6.4​% over 2 ​years, find the interest earned if interest is compounded​ semiannually, quarterly,​ monthly, daily, and continuously.

The interest earned if interest is compounded semiannually is----

​2  

Find the present value of the following future amount.

​$2000 at 10​% compounded annually for 30 years

The present value is-----

3 Suppose a savings and loan pays a nominal rate of

1.4​%

on savings deposits. Find the effective annual yield if interest is compounded quarterly

The effective annual yield is------

4

How long would it take to double your money in an account paying

3​%

compounded quarterly

Ignoring leap​ years, the investment will be doubled in------years and---- days

Answer 1

1. For a deposit of ​$1027 at 6.4​% over 2 ​years, find the interest earned if interest is compounded​ semiannually, quarterly,​ monthly, daily, and continuously.

The interest earned if interest is compounded semiannually is = Effective compounded interest = ( 1 + r / m)n - 1

n = number period we get interest = semiannually of two years = 4

m = how much time compound in a year = 2 = 12 / 6 = 2

Effective compounded interest = ( 1+ 6.4% / 2)4 - 1 = ( 1 + 3.2% )4 - 1 = 1.1342 - 1 = 0.1342 = 13.42%

The interest earned if interest is compounded semiannually is = 1027 * 13.42% = 138

The interest earned if interest is compounded quarterlly is =

n = 2 * 4 = 8

m = 12 / 4 = 4

= (1+ 6.4% / 4)8 - 1 = 1.1354 - 1 = 0.1354 = 13.54%

The interest earned if interest is compounded quarterlly is = 1027 * 13.54% = 139

2. Find the present value of the following future amount. ​$2000 at 10​% compounded annually for 30 years

The present value is-----

PV of Annuity = (A / r )(1 - 1 / ( 1+r)n)

or

PV of Annuity = Amount * ( 1/1+ r)nGT

= 2000 * ( 1/1 + 10%)30GT = 2000 * (1/1.1)30GT = 2000 * 9.4269 = 18854

GT = grand total (calculator fuction)

3. Suppose a savings and loan pays a nominal rate of 1.4​% on savings deposits. Find the effective annual yield if interest is compounded quarterly

The effective annual yield is- = ( 1 + r / n )n  - 1 n =12 /4 = 4

= ( 1 + 1.4% / 4)4 - 1 = ( 1 + 0.35%)4 - 1

= (1.0035)4 - 1

= 1.01407 - 1 = 0.0141  = 1.41%

3. How long would it take to double your money in an account paying 3​% compounded quarterly

Annual effective interest = ( 1 + 3% / 4)4 - 1 = (1+0.75% )4 - 1 = 1.0303 - 1 = 0.0303 = 3.03 %

we can solve it with example, for that we use $ 100 as amt deposite and we need to double our money to $ 200,

For calculation we use a formula

Amount(double the p) = principle ( 1 + r )n

200 = 100 ( 1+ 3.03% )n

Here we need to find the n = number of quarters take to double our money

= 200 / 100 = (1.0303)n  

= 2 = (1.0303)n

Here we use log fuction of calculator

=log 2 / log 1.0302 = n   

n = 23.22 quarters

which mean 23.22 / 4 = 5.805 years

= 5 years and 365 * 0.805 = 294 days

Ignoring leap​ years, the investment will be doubled in --5----years and 294 days