Question

Assume that you are saving up for a trip around the world when you graduate in two years. If you can earn 6% on your investments, how much would you have to deposit today to have $13,500 when you graduate?

Answer 1

$ 12053

Step-by-step explanation:

Interest = [ Principle x Rate x Time ]

Given : Time = 2 years ; Rate = 6% ; Principal = P

Also, Interest = Final Amount - Principal ; & given Final Amount = 13500

13500 - P = [ P x 0.06 x 2 ]

13500 - P = 0.12P

13500 = 0.12 P + P → 1.12P

P = 13500 / 1.12

Principal = 12053

Answer 2

$12,015 approx.

Step-by-step explanation:

To calculate present value of a future amount, the future amount is discounted at the rate of interest for the period of investment, which reveals present value as on today. The technique is referred to as discounting technique.

Suppose P denote the amount invested today, which when matured after period of two years yields $13500. Following formula is used for calculating the money invested:

`A =\ P (1\ +\ (R)/(100)) ^(n)`

wherein, A = Amount

P = Principal

R = Rate of interest

n = number of years

`13500 =\ P (1\ +\ (6)/(100)) ^(2)`

13,500 = 1.1236 P

⇒ P = 12,015 Approx.

Thus, $12015 is required to be deposited today so as to yield $13,500 after 2 years compounded at 6% per annum rate of interest.