Question

What lump sum should be deposited in an account that will earn 11% compounded semi-annual, to grow to

$85,279.73 in 21 years?
The lump sum is
Answer pls

Answer 1

[AI-generated answer — Explain Bot]

To determine the required lump sum, you can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment ($85,279.73 in this case)
P = the principal amount (the lump sum you want to find)
r = the annual interest rate (11% or 0.11)
n = the number of compounding periods per year (semi-annual compounding means n = 2)
t = the number of years (21 in this case)

Now, plug in the given values and solve for P:

$85,279.73 = P(1 + 0.11/2)^(2*21)

Simplifying this equation will yield the value of P:

P = $85,279.73 / ((1 + 0.055)^42)

Calculating this expression:

P = $85,279.73 / (1.055^42)

Using a computer software or calculator to evaluate the expression:

P ≈ $13,235.61

Therefore, a lump sum of approximately $13,235.61 should be deposited to the account in order to grow to $85,279.73 in 21 years at an interest rate of 11% compounded semi-annually.