Answer:
The lump sum amount to be deposited should be $27,020.67
Explanation:
Data provided in the question:
Future value = $60,000
Time, t = 10 years
Interest rate, r = 8% = 0.08
Compounded monthly i.e number of periods n = 12
Now,
Future value = Amount deposited × ![\left( 1 + \frac{r}{n} \right)^{\Large{n \times t}}](https://tex.z-dn.net/?f=%5Cleft%28%201%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%5Cright%29%5E%7B%5CLarge%7Bn%20%5Ctimes%20t%7D%7D)
Therefore,
on substituting the respective values, we get
$60,000 = Amount deposited × ![\left( 1 + \frac{0.08}{12} \right)^{\Large{12 \times 10}}](https://tex.z-dn.net/?f=%5Cleft%28%201%20%2B%20%5Cfrac%7B0.08%7D%7B12%7D%20%5Cright%29%5E%7B%5CLarge%7B12%20%5Ctimes%2010%7D%7D)
or
$60,000 = Amount deposited × ( 1.00667 )¹²⁰
or
$60,000 = Amount deposited × 2.220522
or
Amount deposited = $60,000 ÷ 2.220522
or
Amount deposited = $27,020.67
Hence,
The lump sum amount to be deposited should be $27,020.67