Problem 5-4 Time for a lump sum to double If you deposit money today in an accou

Question

Problem 5-4
Time for a lump sum to double

If you deposit money today in an account that pays 6% annual interest, how long will it take to double your money? Round your answer to two decimal places.

years

Problem 5-14
Future value of an annuity

Find the future values of these ordinary annuities. Compounding occurs once a year. Round your answers to the nearest cent.

Rework previous parts assuming that they are annuities due. Round your answers to the nearest cent.

$200 per year for 4 years at 16%.

$   1013.30

$100 per year for 2 years at 8%.

$   208

$400 per year for 4 years at 0%.

$   1600

$200 per year for 4 years at 16%.

$   ??

$100 per year for 2 years at 8%.

$  ???

$400 per year for 4 years at 0%.

$   1600

Explanation / Answer

There are two types of interests: Simple and compound

In case of simple interest the formula is Principal multiplied by rate of interest multiplied by number of periods.

Rate of interest is 6% and we want to know the number of years in which the sum get doubled which means Interest should be equal to Principal i.e. P = P x .06 x n

Therefore the equation to be solved is 1 = .06 x n or n = 100/6

Therefore the lump sum will become double in 16.67 years if simple interest is paid 6% per annum

Case2: interest is compounded annually the formula in this case is for Amount (principal + interest)

Amount = Principal ( 1 + r/n ) nt

r represents rate of interest and n =no. of times compounded in a year and t stands for no . of years

In the present case we want 2P = P (1 + .06 ) t  

The equation to be solved is: 2 = (1.06) t

The approximate value of t that is number of years is 14 (fourteen)

Answer 5 - 14

Future value of annuity is calculated by repetitive use of Compound interest formula

Future value of $100 per year for 2 years at 8% is = 100 (1 +.08 )1 + 100 ( 1 + .08 )0 = 108 + 100 = 208

Future value of $400 per year for 4 years at 0%is = 400 ( 1+0 ) 3 + 400 ( 1 + 0) 2 + 400(1+0) 1 + 400(1+0) 0

calculated as $1600

Future value

Year Annuity Factor Future value 1 200 1.560896 312.18 2 200 1.3456 269.12 3 200 1.16 232 4 200 1 200 TOTAL 1013.30

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