Brief Exercise 62 Alan Bautista needs 21100 in 6 years What

Brief Exercise 6-2

Alan Bautista needs $21,100 in 6 years.

What amount must he invest today if his investment earns 12% compounded annually? What amount must he invest if his investment earns 12% annual interest compounded quarterly? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)

Solution

Solution:

Part 1 – Investment at 12% annual interest

Total Amount needed in 6 years = $21,100

It is the future value of the amount to be invested today

i.e. Future Value in 6 years = $21,100

Annual Interest 12% means the interest is occurred and paid annually i.e. one time in a year

R = 12% or 0.12

N = 6 times

Hence,

Future Value = Investment amount today x (1 + R)ⁿ

$21,100 = Investment Amount x (1 + 0.12)⁶

$21,100 = Investment Amount x 1.97382

Today’s Investment Amount = $21,100 / 1.97382 = $10,690

Investment at 12% annual interest = $10,690

Part 2 --- Investment at 12% annual interest, compounded quarterly

Interest compounded quarterly means the interest will be paid quarterly i.e. 4 times in a year. So we need to calculate the quarterly Interest Rate and the quarterly number of times

Quarterly Interest Rate (R) = 12% / 4 = 3%

Quarterly Number of times (n) = 6*4 = 24

Future Value = Investment amount today x (1 + R)ⁿ

$21,100 = Investment Amount x (1 + 0.03)²⁴

$21,100 = Investment Amount x 2.03279

Today’s Investment Amount = $21,100 / 2.03279 = $10,380

Investment at 12% annual interest, compounded quarterly = $10,380

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